Volume 4, Number 6

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-                                                                     -
-                                           November 15, 1997        -
-      O P - S F   N E T                    Volume 4, Number 6        -
-      ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~        -
-      Editors:                                                       -
-      Tom H. Koornwinder                   thk@wins.uva.nl           -
-      Martin Muldoon                       muldoon@yorku.ca          -
-                                                                     -
-      The Electronic News Net of the SIAM Activity Group             -
-      on Orthogonal Polynomials and Special Functions                -
-                                                                     -
-                 Please send contributions to:  poly@siam.org        -
-                 & address changes to:  poly-request@siam.org        -
-                                                                     -
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See Topic #26 for new alternative way to subscribe to OP-SF NET.
See Topic #27 for the announcement of a listserv for OP & SF.

Today's Topics:
     1. Tricomi Centennial Conference
     2. Special Functions Day, Amsterdam
     3. Formal Power series and Algebraic Combinatorics -  FPSAC 98
     4. Research Conference in q-Series, Combinatorics and Computer
           Algebra (Massachusetts)
     5. Orthogonal Polynomials: Numerical and Symbolic Algorithms: Madrid
     6. Conference on Lattice Paths Combinatorics and Applications, Vienna
     7. International Workshop on Self-Similar Systems (Dubna)
     8. Reports on SPOA VIII at Sevilla
     9. SPOA Report by Connett and Schwartz
    10. New trends in OP from the Sevilla conference (Kuijlaars)
    11. Impressions from the Sevilla conference (Roesler and Voit)
    12. Recent International Workshop at RIMS, Kyoto
    13. Report on RIMS workshop, Kyoto (Dijkhuizen)
    14. Review of "A = B" by Petkovsek et al.
    15. q-Zeilberger algorithm in Mathematica updated
    16. PhD project on History of Orthogonal Polynomials
    17. "Don't Stop the Problems" (Doron Zeilberger)
    18. Further comments on SIAM Review Problem Section
    19. Comments from SIAM Journals Publisher on Problem and Solutions
    20. Lambert-W function and OPSF Flamesite? (William Gosper)
    21. SIAM Student Paper Prizes
    22. SIAM Student Travel Awards
    23. W.T. and Idalia Reid Prize
    24. Preprint Archive for papers in Orthogonal Polynomials and Special
          Functions (Hans Haubold)
    25. Changes of Address, WWW Pages, etc.
    26. Alternative way to subscribe to OP-SF NET
    27. Starting a new listserv for discussions on OP & SF
    28. Obtaining back issues of OP-SF NET and submitting contributions
         to OP-SF NET and Newsletter

Calendar of Events:

November 28-December 2: Tricomi Centennial Conference,
                       Rome and Turin, Italy                       4.6 #1
December 2: Special Functions Day, Amsterdam, The Netherlands      4.6 #2

March 22-28: Meeting on Applications and Computation of Orthogonal
     Polynomials, Oberwolfach, Germany                             4.3 #6
May 16-22: Symmetries and Integrability of Difference Equations,
     Sabaudia, Italy                                               4.5 #5
June 15-19:  Formal Power Series and Algebraic Combinatorics,
     Toronto, Canada                                               4.6 #3
June 21-25: q-Series, Combinatorics and Computer Algebra,
     South Hadley, Massachusetts, USA                              4.6 #4
June 29-July 2: Workshop on Orthogonal Polynomials: Numerical and Symbolic
     Algorithms, Madrid, Spain                                     4.6 #5
July 8-10: Conference on Lattice Paths Combinatorics and Applications,
     Vienna, Austria                                               4.6 #6
July 13-17: SIAM Annual Meeting, Toronto, Canada
July 30 - August 7: International Workshop on Self-Similar Systems
     Dubna, Russia                                                 4.6 #7

Topic #1   ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Giampietro Allasia <ticam@dm.unito.it>
Subject: Tricomi Centennial Conference

                          TRICOMI's IDEAS

             Convegno Internazionale in occasione del

                    Rome, November 28-29, 1997
                    Turin, December 1-2, 1997

       Purpose of the conference

       The Accademia Nazionale dei Lincei and the Accademia delle
       Scienze di Torino, jointly with the Universita' di Torino and
       the Politecnico di Torino, organize an international conference
       to celebrate the 100th anniversary of the birth of FRANCESCO G.
       The main subjects of the conference will be: Partial Differential
       Equations, Singular Integral Equations, Transonic Aerodynamics,
       Special Functions and Ordinary Differential Equations. The first
       three subjects will be discussed in Rome, while the other two in
       Tricomi's work on these subjects has been of fundamental
       importance and the conference intends to focus the influence of
       Tricomi's ideas in contemporary applied mathematics, giving at
       the same time a picture of the state of the art.

       Organizing Committee:

       G. Allasia, L. Amerio, A. Conte, D. Galletto, L. Gatteschi,
       P. Germain, G. Grioli, E. Magenes, E. Marchi, C. Morawetz,
       S. Nocilla, O. Oleinik, R. Piva, G. Salvini, E. Vesentini.

       Local Organizing Committee (Turin):

       G. Allasia, S. Benenti, A. Conte, R. Conti, D. Galletto,
       B. Gabutti, L. Gatteschi, F. Lerda, R. Malaroda, S. Nocilla,
       F. Skof, E. Vesentini.

       Conference Location:

       Rome, Accademia Nazionale dei Lincei, Palazzo Corsini, Via della
       Lungara 10

       Turin, Universita' degli Studi, Aula Magna, Via Verdi 8
       Accademia delle Scienze di Torino, Via Maria Vittoria 3


            Friday, November 28
            Accademia Nazionale dei Lincei

        9.30  Opening

       10.00  P. GERMAIN (Paris, France): Tricomi problem and fundamental
              solution for Tricomi problem.

       11.00  Coffee-break

       11.15  G. MORETTI (Burlington, Vermont, USA): Lights and shadows
              of transonic aerodynamics across a century.

       12.15  D. GOTTLIEB (Providence, Rhode Island, USA): The use of
              special functions in the numerical solutions of nonlinear
              hyperbolic equations.

       15.00  W. WENDLAND (Stuttgart, Germany): On boundary integral
              equations and applications.

       16.00  Coffee- break

       16.15  J.-C. NEDELEC (Palaiseau, France): The use of integral
              equations for  harmonic Maxwell equations.

       17.15  S. PROESSDORF (Berlin, Germany): Approximation methods for
              integral equations using splines and wavelets.

            Saturday, November 29
            Accademia Nazionale dei Lincei

        9.30  E. I. MOISEEV (Moscow, Russia): On spectral problems for
              the Tricomi equation.

       10.30  G. MONEGATO (Torino, Italy): Numerical resolution of the
              generalized airfoil equation with Possio kernel.

       11.30  Coffee-break

       11.45  O. A. OLEINIK (Moscow, Russia): Free boundary problems for
              backward parabolic equations.

            Monday, December 1
            Aula Magna, Universita' di Torino

        9.30  Opening

       10.00  A. CONTE (Torino, Italy): Francesco G. Tricomi maestro a

       11.50  Coffee-break

       11.20  R. ASKEY (Madison, Wisconsin, USA): Hermite and Laguerre
              polynomials and extensions.

             Accademia delle Scienze di Torino

       15.00  L. GATTESCHI (Torino, Italy): New results on some two-
              dimensional iterative algorithms.

       15.50  B. C. CARLSON (Ames, Iowa, USA): Elliptic integrals:
              symmetry and symbolic integration.

       16.40  Coffee-break

       17.10  N. TEMME (Amsterdam, The Netherlands): Recent problems
              from uniform asymptotic analysis of integrals.

            Tuesday, December 2
            Accademia delle Scienze di Torino

        9.30  W. GAUTSCHI (West Lafayette, Indiana, USA): The incomplete
              gamma function since Tricomi.

       10.20  F. W. J. OLVER (College Park, Maryland, USA): Asymptotic
              and numerical solutions of linear differential equations.

       11.10  Coffee-break

       11.40  J. MAWHIN (Louvain la Neuve, Belgium): The forced pendulum
              equation: a challenging problem for the qualitative theory
              of ordinary differential equations.

            Accademia delle Scienze di Torino

       15.00  F. LERDA (Torino, Italy): Formally linear methods for
              nonlinear ordinary differential equations.

       15.50  F. ZANOLIN (Udine, Italy): Time-maps and boundary value
              problems for ordinary differential equations.

       16.40  Coffee-break

       17.10  E. REGAZZINI (Milano, Italy): Some examples of the
              interplay between special functions and statistics.

      Further information (including registration info):

      e-mail     ticam@dm.unito.it
      fax        +39 11 670 2878   (to Giampietro Allasia)


      Associazione degli Amici dell'Accademia dei Lincei
      Consiglio Nazionale delle Ricerche (Comitato Nazionale per le
      Scienze Matematiche, Gruppo Nazionale Analisi Funzionale e
      Applicazioni, Gruppo Nazionale Fisica Matematica, Gruppo
      Nazionale Informatica Matematica)
      Regione Piemonte
      Fondazione Cassa di Risparmio di Torino
      Fondazione Istituto Bancario San Paolo di Torino

Giampietro Allasia

Topic #2   ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Tom H. Koornwinder <thk@wins.uva.nl>
Subject: Special Functions Day, Amsterdam


Tuesday, 2 December 1997, University of Amsterdam, Department of Mathematics

10.30-11.30:	M. Zygmunt (Warsaw, Poland),
		Matrix moment problem and matrix-valued orthogonal polynomials

12.00-13.00:	S.B. Yakubovich (Minsk, Belarus; temporarily Leuven, Belgium),
		On the variety of integral transformations of the
		Kontorovich-Lebedev type

14.30-15.30:	M. Roesler (Muenchen, Germany),
		Positivity of Dunkl's intertwining operator

16.00-17.00:	S.O. Warnaar (Amsterdam),
		The Bailey Lemma

Location: building Euclides, room P015A, Plantage Muidergracht 24, Amsterdam

Organizer: Tom H. Koornwinder, UvA, tel. 020-525 5297, email thk@wins.uva.nl

Financial support has been given by Stichting Wiskunde Onderzoek Nederland

Further information:

Tom Koornwinder

Topic #3   ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Nantel Bergeron <bergeron@mathstat.yorku.ca>
Subject: Formal Power series and Algebraic Combinatorics -  FPSAC 98

% ********************************************************************** %
%                                                                        %
%           10-th international Conference on                            %
%           Formal Power Series and Algebraic Combinatorics              %
%                                                                        %
%           June 15-19, 1998                                             %
%           Fields Institute, Toronto                                    %
%                                                                        %
%           First announcement -- Call for papers                        %
%                                                                        %
% ********************************************************************** %

TOPICS: Algebraic and bijective combinatorics and their relations with
other parts of mathematics, computer science and physics.

CONFERENCE PROGRAM: Invited lectures, contributed presentations,
poster session, software demonstrations.

              G. Benkart   (USA)
              P. Cameron   (England)  (to be confirmed)
              P. Dehornoy  (France)
              B. Derrida   (France)   (to be confirmed)
              P. Diaconis  (USA)
              C. Godsil    (Canada)
              K. Ono       (USA)
              J. Y. Thibon (France)
              B. Sturmfels (USA)

OFFICIAL LANGUAGES: English and French.

CALL FOR PAPERS AND POSTERS: Authors are invited to submit extended
abstracts of at most twelve pages before

                November 21, 1997.

Authors should indicate their choice of presentation appropriate for their
paper: lecture or poster session. The preferred method of submission is by
sending one postscript file by email to


If an author is not able to send a postscript version of her/his extended
abstract, four copies of the extended abstract should be mailed to

     Nantel Bergeron, Program committee of FPSAC '98
     Department of Mathematics and Statistics 61
     York University
     4700 Keele St.
     North York, Ontario, Canada, M3J 1P3.

The submitted papers should begin with a summary written in the two
official languages of the conference (translations will be provided if
necessary). The notifications of acceptance or rejection are scheduled for
the beginning of March 1998.

Published Volume:
The authors whose papers will have been accepted for a lecture or a poster
presentation will have the possibility to submit a complete version of
their work to a special issue of a refereed publication devoted to the
conference FPSAC '98. The deadline for submission to the special issue is
September 1, 1998.

SOFTWARE DEMONSTRATIONS: Demonstrations of software relevant to the topics
of the conference are encouraged. People interested in giving a software
demonstration should submit a paper as described above, including the
hardware requirements, before January 15, 1997, by email to


I. Goulden, Chairman (Canada), N. Bergeron (Canada), S. Billey (USA),
F. Brenti (Italy), R. Cori (France), S. Dulucq (France)
K. Eriksson (Sweden), O. Foda (Australia), S. Fomin (USA/Russia),
I. Gessel (USA), C. Greene (USA), A. Hamel (New Zealand), D. Kim (Korea),
C. Krattenthaler (Austria), D. Krob (France), M. Noy (Spain), V. Reiner (USA),
C. Reutenauer (UQAM), F. Sottile (U. Toronto), T. Visentin (U. Winnipeg).
M. Wachs (USA), H. Yamada (Japan), G. Ziegler (Germany).

For more Information on registration and support, consult the WWW site


or email


N. Bergeron, Chairman (York U.), M. Delest (U. de Bordeaux),
F. Sottile (U. Toronto), W. Whiteley (York U.).

Nantel Bergeron

Topic #4   ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: OP-SF NET Editor <muldoon@yorku.ca>
Subject: Research Conference in q-Series, Combinatorics and Computer

As one of the "Joint Summer Research Conferences in the Mathematical
Sciences", a Conference on "q-Series, Combinatorics and Computer Algebra"
will be held at Mount Holyoke College, South Hadley, Massachusetts, USA,
June 21-25, 1998.  The co-chairs are Mourad Ismail
(ismail@math.usf.edu) and Dennis Stanton (stanton@math.umn.edu).

The topics to be covered will include:
(1) classical q-series, number theory and orthogonal polynomials,
(2) multivariable polynomials and quantum groups,
(3) applications of computer algebra packages to combinatorial problems,
(4) applications of q-series to physical problems.

Preliminary list of speakers:
George Andrews
Richard Askey
Pavel Etinghof
Dominique Foata
George Gasper
Ira Gessel
R. William Gosper
Christian Krattenthaler
Tom Koornwinder
Steve Milne
Ken Ono
Doron Zeilberger

Those interested in attending and in possible financial support should
contact the Summer Research Conference Coordinator, American Mathematical
Society (e-mail: rgc@ams.org).

The above information is summarized from the print version of the Notices
of the American Mathematical Society, November 1997, pp. 1412-1414.
However, the list of topics and speakers for this conference is mistakenly
transposed to the announcement of the conference on "Geometric Group
Theory and Computer Science" (July 5-9).

Topic #5   ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Renato Alvarez-Nodarse <renato@dulcinea.uc3m.es>
Subject: Orthogonal Polynomials: Numerical and Symbolic Algorithms

International Workshop on Orthogonal Polynomials:
Numerical and Symbolic Algorithms, Madrid, June 29-July 2, 1998

First announcement

It is well-known that increasing attention has been paid in recent years
to the theory of Orthogonal Polynomials. This is due, in particular, to
their applications in areas like numerical integration, spectral methods,
interpolation, approximation theory, etc. and also in combinatorics,
mathematical physics, quantum physics, etc. For this reason the
Universidad Carlos III de Madrid organizes an international workshop
devoted to this topic every two years. The first workshop in 1992 was
dedicated to Sobolev orthogonal polynomials, the second, in 1994 to
polynomials orthogonal in the unit circle, and the most recent one, in
1996, to the applications of orthogonal polynomials in mathematical

The main aim of the next (1998)  Workshop is that a relatively small
number of invited mathematicians discuss and review recent progress of the
Theory of Orthogonal Polynomials with special emphasis on numerical
applications and symbolic algorithms. The Workshop will take place in the
main building of the Escuela Politecnica Superior, Universidad Carlos III
de Madrid, Leganes (Madrid).

The topics to be considered will be:
1. Quadrature formulas
2. Spectral methods in boundary value problems
3. Numerical Linear Algebra
4. Symbolic algorithms and software
5. Combinatorics

It will be possible for interested participants to present their own
contributions in the above mentioned areas. Because the limited number of
short communications we ask participants who want to present their works
to send us, as soon as possible (March 31, 1998), the abstract (no more
than one page).  Priority will be given to those talks closely related to
the main subject of the Workshop.

The invited speakers  are:
- Walter Gautschi (Purdue University, USA)
- Gene Golub (Stanford University, USA)
- Wolfram Koepf (Konrad-Zuse-Zentrum, Berlin, Germany)
- Yvon Maday (Universite Pierre et Marie Curie, France)
- Marko Petkovsek (University of Ljubljana, Slovenia)
- Doron Zeilberger (Temple University, USA)

The Proceedings: We will prepare a special monograph containing the
Proceedings of the Workshop.

Registration fee: 15.000 ptas.; includes lunch and the Proceedings.

The Organizing Committee is:
- M. Alfaro (Univ. de Zaragoza),
- R. Alvarez-Nodarse (Secretary) (Univ. Carlos III),
- J. Arvesu (Univ. Carlos III),
- F. Marcellan (Chairman) (Univ. Carlos III).

The Scientific  Committee is:
- R. Alvarez-Nodarse  (Univ. Carlos III),
- J. S. Dehesa (Univ. de Granada),
- E. Godoy (Univ. de Vigo),
- G. Lopez Lagomasino (Univ. Carlos III),
- F. Marcellan (Chairman) (Univ. Carlos III) and
- A. Zarzo (Univ. Politecnica de Madrid).

Invited Talks (60 min.):
- Walter Gautschi, "Orthogonal Polynomials and
   Quadrature" and "Rational Gauss-type Quadrature Rules"
- Gene Golub,  "Matrices, moments and quadrature" and
   "Solution of regularized systems"
- Wolfram Koepf, "Software for the Algorithmic Work with Orthogonal
   Polynomials and Special Functions"
- Marko Petkovsek, no title yet
- Doron Zeilberger, "The Unreasonable Power of Orthogonal Polynomials in
   Combinatorics, I and II"
- Yvon Maday, no title yet

To get more information please contact:

R. Alvarez-Nodarse
F. Marcellan
Departamento de Matematicas
Escuela Politecnica Superior
Universidad Carlos III de Madrid
Butarque 15, 28911, Leganes, Madrid
fax: +34-1 624-94-30
phone: +34-1 624-94-70, +34-1 624-94-42
e-mail: iwop98@dulcinea.uc3m.es

For updated information visit the IWOP'98 WWW page


On http://dulcinea.uc3m.es/users/workshop/iwop96.html

you will find information about the most recent Workshop on Orthogonal
Polynomials held in Leganes on June 24-26, 1996.

R. Alvarez-Nodarse

Topic #6   ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Walter B"ohm <boehm@wu-wien.ac.at>
Subject: Conference on Lattice Paths Combinatorics and Applications, Vienna

*                   4th International Conference on                      *
*             Lattice Paths Combinatorics and Applications               *
*                                                                        *
*                 First announcement -- Call for papers                  *
*                                                                        *
*                             July 8-10, 1998                            *
*                                                                        *
*                  University of Vienna, Vienna, Austria                 *
*                                                                        *
*              This conference is dedicated to the Memory of             *
*                              T.V. Narayana.                            *
*                                                                        *

Topics to be covered by the conference include

  o   lattice paths and boundaries
  o   plane partitions
  o   Young tableaux
  o   q-calculus
  o   orthogonal polynomials
  o   random walk problems
  o   nonparametric statistical inference
  o   discrete distributions and urn models
  o   queueing theory
  o   analysis of algorithms

Submission of papers:

Authors are invited to submit abstracts of at most four pages before
February 1, 1998. Preferred way of submission is by sending ONE postscript
file by email to boehm@isis.wu-wien.ac.at.

If an author is not able to send a postscript version of her/his extended
abstract, four copies of the extended abstract should be mailed to Walter
B"ohm, Department of Statistics, University of Economics and Business
Administration, Augasse 2-6, A-1091 Vienna, Austria. Authors are also
requested to indicate how much time they will need to present their talks.

The complete versions of the papers to be presented should be received not
later than July 10, 1998. After a standard refereeing process papers
accepted by the scientific committee will be published in a special issue
of the Journal of Statistical Planning and Inference.


The conference will take place at the Institut f"ur Mathematik of the
Universit"at Wien. The first talk is scheduled on July 8, 1998 at 9:00

Organizing committee:
W. B"ohm, University of Economics, Vienna, Austria
Ch. Krattenthaler, University of Vienna, Austria
S.G. Mohanty, McMaster University, Canada
K. Sen, University of Delhi, India

Scientific committee
N. Balakrishnan, McMaster University, Canada
Ch. Charalambides, University of Athens, Greece
E. Csaki, Hungarian Academy of Science, Hungary
I. Gessel, Brandeis University, U.S.A.
A.W. Kemp, University of St. Andrews, Scotland
C.D. Kemp, University of St. Andrews, Scotland
S.G. Mohanty, McMaster University, Canada
H. Niederhausen, Atlantic University, U.S.A.

Further Information:

A WWW site http://www.wu-wien.ac.at/wwwu/institute/stat1/lp/lp.html
has been set up for the conference which will always contain the
latest state of affairs.

For any further question, please just write to

Walter B"ohm, Department of Statistics, University of Economics and Business
Administration, Augasse 2-6, A-1091 Vienna, Austria.

Tel.: +43-1-31336/4755, Fax: +43-1-31336/774,
E-mail: boehm@isis.wu-wien.ac.at.

Topic #7   ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Vyacheslav Spiridonov <svp@thsun1.jinr.dubna.su>
Subject: International Workshop on Self-Similar Systems

                       FIRST ANNOUNCEMENT
               International Workshop "SELF-SIMILAR SYSTEMS"
                 Dubna, Russia, July 30 - August 7, 1998


 The Bogoliubov Laboratory of Theoretical Physics of the Joint
 Institute for Nuclear Research organizes an International Workshop
 'Self-similar systems'. The workshop will be held in Dubna, a
 small quiet town surrounded by forest on the bank of the Volga
 river, 120 km north of Moscow. It will start on Thursday morning
 July 30 and end Friday August 7, 1998.

 The Workshop will be devoted to diverse aspects of self-similar systems.
 The main attention will be paid to mathematically justified theories (the
 wavelet analysis, solvable models of self-organized criticality,
 quasicrystals, etc). There will be a special session (around 5-6 August)
 devoted to the commemoration of the centenary of Ya. L. Geronimus. This
 will put a particular emphasis upon orthogonal polynomials (general theory
 and classical, semi-classical, Laguerre-Hahn polynomials, etc).

 An expected number of participants is 50-60, including a number of people
 invited by organizers and students. There will be review lectures of 45 min
 and shorter special seminars for experts. Selection of talks is by the
 advisory and organizing committees. Due to the interdisciplinary character
 of the workshop, there will be introductory mini-courses: "Time-frequency
 analysis and wavelets" by B. Torresani, "Wavelets and multifractals"
 by S. Jaffard and "Discretizations in Lie groups" by A. Iserles.

 - Wavelets and other self-similar functions
 - Self-organized criticality
 - Multifractals
 - Orthogonal polynomials
 - Eigenvalue problems with the singular continuous spectra
 - Quasicrystals
 - Self-structuring phenomena and turbulence
 - Difference equations and numerical methods

  R. Askey (Madison)           D. Dhar (Bombay)
  A. Iserles (Cambridge)       S. Jaffard (Paris)
  V.K. Mel'nikov (Dubna)       J. Patera (Montreal)
  M. Schroeder (Gottingen)     A.N. Sharkovsky (Kiev)
  K. Sneppen (Copenhagen)

 V.B. Priezzhev  (BLTP JINR)   priezzvb@thsun1.jinr.ru
 V.P. Spiridonov (BLTP JINR)   svp@thsun1.jinr.ru
 A.L. Baranovski (LCTA JINR)
 L.B. Golinskii  (ILT, Kharkov)
 E.N. Rusakovich (JINR Internat. Dept.)
 A.M. Povolotsky (BLTP JINR) - Scientific secretary

 APPLICATION:   A registration form is attached. It should be returned
                to the Scientific secretary by e-mail povam@thsun1.jinr.ru
                not later than March 31, 1998.

 POST ADDRESS:   Prof. V.B. Priezzhev or Dr. V.P. Spiridonov
                 Bogoliubov Laboratory of Theoretical Physics
                 Joint Institute for Nuclear Research
                 141980 Dubna, Moscow region, RUSSIA
 FAX:            (7-09621) 6-50-84
 INTERNET:       http://thsun1.jinr.ru/meetings/

 The Workshop fee for 10 days is 450 USD. It includes transportation from
 Moscow airports (or train stations) to Dubna (2 hours drive) and back,
 hotel accommodations (rates for double occupancy), coffee breaks, reception
 and a social program. For those who cannot participate for full length the
 fee will be reduced by an appropriate amount. The fee for accompany persons
 is 200 USD. The number of supporting grants for students will be determined
 after obtaining responses from funding organizations. The fee will be
 accepted in cash during the registration in Dubna.

********************* REGISTRATION FORM **********************
        The International Workshop "SELF-SIMILAR SYSTEMS"
               Dubna, Russia, July 30 - August 7, 1998

 NAME: .................. FIRST NAME: ...........................
 I would like to give a talk (title and a short abstract): ......
 Affiliation (address), position: ...............................
 Phone:..................... Fax: ...............................
 E-mail: ........................................................

 Further details and the visa application form will be sent separately.
 Please return to M.A. Povolotsky by e-mail povam@thsun1.jinr.ru
 or fax (7-09621) 6-50-84.

Topic #8   ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: OP-SF NET Editor <thk@wins.uva.nl>
Subject: Reports on SPOA VIII at Sevilla

The VIII Simposium sobre Polinomios Ortogonales y sus Aplicaciones was
held in Sevilla during 22-26 September 1997.  It is the eighth in a line
of symposia on orthogonal polynomials and their applications which are
held in Spain once a year. But it fits also into a series of major
European conferences on orthogonal polynomials (Bar-le-Duc, Segovia,
Erice, Delft, Sevilla). In particular, conferences of this last series try
to offer a state of the art, although no conference nowadays will cover
the whole are of orthogonal polynomials and special functions. Therefore
it seemed appropriate to ask a few people to report on the Sevilla
conference.  Bill Connett and Alan Schwartz describe the general setting.
Next Arno Kuijlaars on the one hand and Margit Roesler and Michael Voit on
the other hand discuss, each from their own specialism and taste, the
scientific trends which became apparent from the lectures in Sevilla.

Topic #9   ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Bill Connett <connett@arch.umsl.edu>
      and Alan Schwartz <schwartz@arch.cs.umsl.edu>
Subject: Report on SPOA VIII at Sevilla


Facultad de Matematicas
Universidad de Sevilla
Sevilla, 22-26 September 1997

This international conference had approximately 150 registrants. It
featured ten plenary talks and approximately 70 talks in the research
seminars. It also included the most memorable opening session in recent
memory. This session took place in the main university building which was
formerly the tobacco factory made famous in the opera Carmen. The Chairman
of the Organizing Committee, Professor Duran, entertained us with a list
of the organizations that had promised support for this conference, and
expressed his gratitude for that support, carefully titrated to reflect
the degree to which the organizations had fulfilled their promises.  This
candor was very much appreciated by those members of the audience that had
struggled with similar problems in the past. The Vice-Rector of the
University then gave an elegant and emotional speech comparing the
researchers' pursuit of mathematics to Don Pedro's pursuit of Carmen, with
a number of interesting asides about the complexity and volatility of our
beloved mathematics, and the dangers inherent in the pursuit of such a coy
and demanding muse. In any event, the audience was afire with passion, and
greeted the first plenary speaker, Herbert Stahl, as the young matador
leading the corrida. We were not disappointed, Professor Stahl gave an
elegant and enlightening performance.

This was a very full meeting with sessions from 9:30 in the morning until
6:00 or 7:00 in the evening, but the organizers fitted in three very
pleasant events. The participants were treated to an evening tour of the
Cathedral (third largest in Europe), the Giralda tower (the bell tower,
formerly a mosque), Los Reales Alcazares (the Mudjehar Royal Palace) and
the Bario de Santa Cruz (former Jewish quarter), so we had ample
opportunity to contemplate Spain's Muslim, Jewish and Christian Heritage.
The conference dinner, a sumptuous affair, took place in the Gardens of
Villa Luisa. An evening of Flamenco was provided for Friday night. Of
course, many extracurricular excursions were mounted to sample the
delights of this wonderful city.  The program of plenary talks:

- Daniel Alpay, "Exact formulas for continuous and discrete orthogonal
polynomials with rational weights and applications to solutions of
inverse spectral problem"

- Alexandre Aptekarev, "Asymptotics of general multiple orthogonal

- Richard Askey, "Combinatorics of the classical orthogonal polynomials"

- T. H. Koornwinder, "A survey of symbolic computation for orthogonal
polynomials and special functions"

- A. L. Levin and D. S. Lubinsky (speaker), "Orthogonal polynomials for
exponential weights"

- A. Martinez, "Asymptotic properties of Sobolev orthogonal polynomials"

- E. A. Rakhmanov, "Constrained equilibrium measure and zero distribution
of discrete orthogonal polynomials"

- E. B. Saff, "Zeros of orthogonal polynomials"

- Herbert Stahl, "Spurious poles of Pade approximants"

- Vilmos Totik, "Orthogonal polynomials with respect to varying weights
and the so called universality law"

Special mention must be make of Professor Lubinsky's presentation, which
set a new and very high standard for multimedia presentations.  Every
theorem by a famous person was accompanied with an historic photograph or
drawing, and the mathematics wizard managed to place an interesting and
appropriate cartoon on every slide, frequently drawing attention to some
of the more surprising moments in the line of argument.  This sets the new
standard in presentation which Doron Zeilberger can now aim for.

All the participants were grateful for the efforts made by the organizing
committee A.J. Duran, P. Lopez-Rodriguez, and J.C. Medem of the University
of Sevilla. The gratitude extended beyond their efforts in organizing the
meeting, providing comfortable accommodations, and arranging the cultural
events. We are all grateful for the opportunity to visit this beautiful
old city.

William C. Connett and Alan L. Schwartz

Topic #10  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Arno Kuijlaars <maarno@math.cityu.edu.hk>
Subject: New trends in OP from the Sevilla conference

New trends in orthogonal polynomials from the Sevilla conference

    The impression from the Sevilla meeting is that the field of
orthogonal polynomials is still very much alive.  A number of new
directions have appeared where new results were obtained and more
developments are to be expected.  Of course, my impression is biased by my
own interests, which is in asymptotics. This area was very well
represented in Sevilla and in the plenary talks in particular.
    E.A. Rakhamnov reported on his very elegant results on asymptotics for
polynomials satisfying a discrete orthogonality. This work has already
attracted a number of follow-up papers, and the interest is continuing to
grow, especially in the direction of strong asymptotics.
    Another direction that has grown in importance over the last few
years, is the theory of matrix orthogonal polynomials, as witnessed by the
plenary talks of D. Alpay and E.B. Saff.
    There is continuing interest in the theory of Sobolev orthogonal
polynomials, with main contributions from the large and active Spanish
school. A review on asymptotic results was presented by A. Martinez. It is
clear that progress has been made in recent years.
    Multiple orthogonality has been a favourite with the Russian school.
It deserves wider interest, because of its connections with simultaneous
Pade approximation and irrationality proofs in number theory. The topic
was reviewed by A. Aptekarev.
    Of basic importance remain the applications of orthogonal polynomials
in mathematical physics. Relations with integrable systems and random
matrices were discussed in a number of talks (e.g. Chen, Grunbaum,
Kaliaguine, Totik). One of the highlights of the Sevilla meeting was V.
Totik's announcement of a proof of the universality conjecture in random
matrices using clever estimates on orthogonal polynomials. This kind of
interaction with other areas keeps our field alive.

Arno Kuijlaars

Topic #11  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Margit Roesler <roesler@mathematik.tu-muenchen.de> and Michael Voit
Subject: Impressions from the Sevilla conference

Impressions from the Sevilla conference

This symposium has its roots in a series of Spanish meetings during the
1980's. Since then, it has become a constantly growing international
meeting ground for scientists working on special functions and their
applications. The present meeting was attended by about 150 participants
from all over the world.

There were 10 one-hour plenary talks (see the list in the report of Bill
Connett and Alan Schwartz), and about 70 research talks which were held in
four parallel sessions. In fact, the program was quite dense, and it was
often difficult for us to decide in which session we should attend.
Nevertheless, we had the impression that the arrangement of the sessions
was carefully planned; as far as possible, the afternoon sessions were
dedicated to particular topics. Here the variety was very broad: there
were sessions on more classical aspects of orthogonal polynomials
including asymptotics, zeros, and moment problems, as well as Sobolev
orthogonal polynomials, q-special functions, and multivariable aspects.
Several sections were devoted to applications in approximation theory,
differential equations, mathematical physics, and probability theory.
Finally, a special computer algebra session was organized by SCAGOP
(Spanish Computer Algebra Group on Orthogonal Polynomials).

Compared to earlier conferences of this kind (like Delft or Granada), we
here in particular enjoyed a growing emphasis on multivariable structures
and a strong impact from problems in mathematical physics and probability
theory. As usual at conferences of this size, the scientific level of the
talks was varied. Among the plenary lectures, we were in particular
impressed by the opening lecture of Herbert Stahl and the excellent
performance of Doron Lubinsky.

The organization of the symposium was almost perfect - except for the
queues at the computer facilities. Most participants were conveniently
accommodated at the Residence Hernando Colon. Besides the intense
scientific part of the conference, an extraordinary program of social
activities was offered; here we especially remember the conference
dinner in the Gardens of Villa Luisa and the (almost?) authentic
Flamenco show on Friday night. The organizing committee, consisting of
A.J. Duran, P. Lopez-Rodriguez, and J.C. Medem, has really done a great

Margit Roesler and Michael Voit

Topic #12  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: OP-SF NET Editor <thk@wins.uva.nl>
Subject: Recent International Workshop at RIMS, Kyoto

At RIMS (Research Institute of Mathematical Science, Kyoto, Japan) an
international workshop on "Invariant Differential Operators, Special
Functions and Representation Theory" was held during October 20-31, 1997.
The organizer was Toshio Oshima (University of Tokyo).  I take the
following information from the URL
In the next Topic Mathijs Dijkhuizen, who participated, will give a

One half of the workshop (the second week) was devoted to
"Integrable systems of difference and differential equations"
The main speakers, with series of 3 or 4 lectures each, were

Eric M. Opdam (Leiden Univ.): Dunkl Operators
In these lectures I will give an overview of results on Dunkl's
"differential-reflection" operators, up to the most recent developments.
Mainly I will concentrate on the (differential)  trigonometric case, the
case of the Dunkl-Cherednik operators, because in this case the theory has
reached the most mature level at present. And also there are several older
theorems and applications whose proofs can be polished by modern methods,
but many of these things were never written. So I feel that giving such a
series of lectures can be rewarding, and I am happy to embark on such a
project. Roughly, I have in mind to treat the following subjects:

Knizhnik-Zamolodchikov connection, the Harish-Chandra system, monodromy
representation, the shifting principle, asymptotic expansions, the Gauss'
summation formula.
  2. ALGEBRAIC PROPERTIES. Nonsymmetric orthogonal polynomials, the graded
Hecke algebra, (affine) intertwiners, the recursion formula of Knop and
  3. HARMONIC ANALYSIS. The Fourier transform for the Dunkl-Cherednik
operators, the Paley Wiener theorem, the action of the affine Weyl group.
  4. RESIDUE CALCULUS FOR ROOT SYSTEMS. The Plancherel measure for the
attractive case; classification of all square integrable eigenfunctions,
and their explicit norms.

S. Ruijsenaars (CWI, Amsterdam):
Special functions solving analytic difference equations

   * I Generalized gamma functions
   * II A generalized hypergeometric function
   * III Generalized Lame functions

I. We discuss a new solution method for difference equations of the form
F(z+ia/2)/F(z-ia/2) = Phi(z), with Phi(z) meromorphic and free of zeros
and poles in a strip |Im(z)| < C. The method gives rise to generalized
gamma functions of hyperbolic, elliptic and trigonometric type (Euler's
gamma function being of rational type), whose properties we sketch.

II. The hyperbolic gamma function can be used as a building block to
construct a novel generalization of the hypergeometric function _2 F_1 .
The new function is a simultaneous eigenfunction of four independent
hyperbolic difference operators of Askey-Wilson type. The integral
representation through which this joint eigenfunction is defined
generalizes the Barnes representation for _2 F_1. It is meromorphic and
has various remarkable symmetry properties that are not preserved for its
q -> 1 ( or `nonrelativistic') limit _2 F_1.

III. The `q=1/nonrelativistic' Lame differential operator can be
generalized to a `q \ne 1/relativistic' difference operator. (The latter
may be viewed as the Hamiltonian defining the elliptic relativistic
Calogero-Moser N-particle system for N=2.) We present eigenfunctions of
this operator. They are in fact joint eigenfunctions of three independent
difference operators. The functions are used to define the Hamiltonian as
a self-adjoint operator on a Hilbert space. Their asymptotics is governed
by a c-function that is a quotient of two elliptic gamma functions.

Topic #13  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Mathijs S. Dijkhuizen <msdz@math.s.kobe-u.ac.jp>
Subject: Report on RIMS workshop, Kyoto


The international workshop at RIMS late October was part of the scientific
activities organized in the framework of a special Research Project on
Representation Theory.  Most of the activities are concentrated in the
autumn. The project includes the invitation of a number of foreign
researchers to RIMS for a more or less extended period.  The two
distinguished visitors this autumn are Prof. Grigori Olshanski (Moscow)
and Prof. Eric Opdam (Leiden), who are staying here for four months.

The workshop was split into two parts. The first week was devoted to
representation theory and featured two series of lectures by Olshanski (on
combinatorial and probabilistic aspects of harmonic analysis on big, i.e.
infinite-dimensional, groups) and Prof. Michael Eastwood (Adelaide, on
invariant differential operators on homogeneous spaces)  plus a number of
other talks. During the second week the topic was integrable systems of
difference and differential equations. Since I did not attend the first
part of the workshop, I will restrict myself to some comments about the
second part. As suggested by the topic, most of the talks were somehow
concerned with systems of commuting operators. The two main speakers were
Eric Opdam and Prof. Simon Ruijsenaars (Amsterdam), who each gave three or
four one-hour talks.

Opdam talked about trigonometric Dunkl operators and their use in the
study of multivariable hypergeometric functions associated with root
systems. Hypergeometric functions in one variable have been known for a
very long time; the earliest indications how to generalize them to many
variables came from representation theory, where they arise as zonal
spherical functions on Riemannian symmetric spaces. The notion of Dunkl
operator, however, is something completely new which is not all hinted at
by the connection with Riemannian symmetric spaces. Dunkl wrote down his
original differential-reflection operators with rational coefficients
around 1989.  One of their main properties is that they commute with each
other. A trigonometric version of these operators was introduced by
Cherednik who related them to the degenerate affine Hecke algebra. The
importance of Dunkl operators for the theory of hypergeometric functions
is explained by the fact that they allow one to give an elementary
algebraic construction of the commuting system of hypergeometric
differential operators for arbitrary values of the coupling constants. The
existence of this hypergeometric system was established earlier by Heckman
and Opdam using analytic methods. Over the last couple of years a whole
body of theory has developed around Dunkl operators.

Opdam's talk was phrased in the elegant language of arbitrary reduced root
systems and Weyl groups. This was in quite some contrast with Ruijsenaars'
series of lectures, which, though certainly no less interesting, was
characterized by a rather down-to-earth approach to a one-variable
problem, namely the study of meromorphic solutions of certain types of
analytic difference equations. Ruijsenaars actually started by remarking
that an analyst from the late nineteenth century would have had no problem
following at least the first part of his talks. Analytic difference
operators were studied by several distinguished mathematicians until less
than a hundred years ago, but later they failed to attract much interest.
This seems to be changing now.  Due to a notable lack of general theory
about solutions of analytic difference equations most results have to be
proved "by hand". One striking feature is the (rather obvious) fact that
the solution space is usually infinite-dimensional. By imposing certain
conditions on the asymptotic behaviour of the solution one can, however,
arrive at certain uniqueness results. Ruijsenaars' motivation for studying
these analytic difference equations partly comes from relativistic
analogues of the quantum integrable Calogero-Moser-Sutherland models for N
interacting particles on the real line. The trigonometric versions of
these relativistic quantum models may be regarded as a q-analogue of the
hypergeometric system discussed by Opdam. As shown by Cherednik, their
algebraic properties are also amenable to a Dunkl operator approach. The
polynomial solutions of these systems have been studied by Macdonald and
others (for reduced root systems) and Koornwinder, Van Diejen, Noumi and
others in the BC_n case (in the one-variable case they reduce to
well-known families of q-hypergeometric polynomials of Askey-Wilson type).
These polynomials are also known to occur in connection with quantum
groups. As for non-polynomial solutions of these systems, not much is
known at this time. As is apparent from Ruijsenaars' talks, a lot of
interesting work in this direction is still waiting to be done.

In short, this was a very stimulating workshop with some very
interesting mathematics.

Mathijs S. Dijkhuizen

Topic #14  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Wolfram Koepf <koepf@zib.de>
Subject: Review of "A = B" by Petkovsek et al.

"A = B" by Marko Petkovsek, Herbert S. Wilf and Doron Zeilberger,
AK Peters, Wellesley, 1996, $39.00. xii + 212 pp., ISBN 1-56881-063-6.

(Editors' Note: This review is reprinted with permission from SIAM Review,
Volume 39, Number 3, pages 538-540, copyright 1997 by the Society for
Industrial and Applied Mathematics. It appeared in our printed Newsletter,
vol 8, no 1, October 1997, pages 11-13.)

In their recent research, the authors of the book under review have given
important contributions towards computer proofs of hypergeometric identities.
Hypergeometric identities are identites about hypergeometric sums, i.e.,
definite sums

                     S_n:=sum_{k in Z} F(n,k)                    (1)

where the summand is a hypergeometric term with respect to both n and k,
i.e.,  the term ratios

              F(n+1,k)/F(n,k)  and   F(n,k+1)/F(n,k)

are rational functions in n and k.

In the book under review, this knowledge is collected, and a nice
introduction to the topic is given.

The main idea behind these computerized proofs is to detect a
_holonomic_recurrence_equation_ for the sum S_n under consideration, i.e.,
a linear recurrence equation with polynomial coefficients.  Zeilberger was
the one having the idea how to adjust Gosper's algorithm on indefinite
hypergeometric summation to the definite case.

Although many of these ideas can be generalized, e.g., towards the
consideration of multiple sums, integrals, q-sums, the generation of
differential rather than recurrence equations, etc., the authors are
mainly concerned with the above mentioned setting.

The contents of the book follow:

The foreword is written by Donald Knuth. He gives some examples of sums
which he was investigating, and for which the new methods are great tools.
The funny thing is that his main example,

       S_n = sum_{k in Z} {2n-2k choose n-k}^2 {2n choose k}^2

is slightly corrupted by a typographical error.  This one has a recurrence
equation whose printout covers a whole page, which shows the power and the
pitfalls of Zeilberger's method at the same time!  The sum Knuth really
meant is the much more well-behaved equation

       S_n = sum_{k in Z} {2n-2k choose n-k}^2 {2k choose k}^2

which satisfies the simple recurrence equation

0 = (n + 2)^3 S_{n+2} - 8(3 + 2n)(2n^2 + 6n + 5)S_{n+1} + 256(n+1)^3 S_n.

Note that an errata sheet can be found at the URL

A Quick Start...: Here, by a short example, it is shown how to download
software in Maple and Mathematica from the World Wide Web, and how to deal
with this software.

I Background

1. Proof machines:
Canonical and normal forms are discussed, and it is shown how proofs can
be given ``by examples,'' using recurrence equations as normal forms.
Polynomial, trigonometric, and other types of identities are discussed.

2. Tightening the target:
Here the main topic of the book, the _hypergeometric_identities_, are
introduced. It is shown how Mathematica and Maple deal with hypergeometric
sums, and WZ proof certificates (see Chapter 7) are introduced.

3. The hypergeometric database:
A database of hypergeometric identities can be used to identify sums as
soon as such sums are converted into hypergeometric notation. Here this
conversion is considered.

II The five basic algorithms

4. Sister Celine's method:
Celine Fasenmyer's method of finding a recurrence equation with respect to
n for a sum S_n given by (1) is presented. Celine Fasenmyer uses linear
algebra to detect a k-free recurrence equation with respect to both n and
k for the _summand_, which afterwards is summed resulting in the
recurrence equation searched for.

5. Gosper's algorithm:
Gosper's algorithm finds a hypergeometric term antidifference s_k for a_k,
i.e., s_{k+1}-s_k=a_k, whenever such an antidifference exists.  As a
result, indefinite summation of hypergeometric terms can be treated

6. Zeilberger's algorithm:
Zeilberger's algorithm uses a variant of Gosper's algorithm to determine
holonomic recurrence equations for definite sums, given by (1). In most
cases this recurrence equation is of lowest order. If it is of first
order, then one can read off the hypergeometric term solution; if it is
not, Petkovsek's algorithm, described in Chapter 8, can be used to
determine such solutions if applicable.

Note that Zeilberger's algorithm in general is much faster than Celine
Fasenmyer's method since its linear algebra part deals with mainly J+1
rather than with (J+1)^2 variables if J denotes the order of the
recurrence equation searched for.

7. The WZ phenomenon:
In the cases in which Zeilberger's algorithm determines a first order
recurrence equation, the WZ phenomenon occurs: such a hypergeometric
identity can be proved by bringing it into the form

                     S_n:=sum_{k in Z} F(n,k) = 1                   (2)

and by using Gosper's algorithm to find a rational multiple G(n,k) =
R(n,k) F(n,k) of F(n,k) for which

                F(n+1,k)-F(n,k) = G(n,k+1)-G(n,k).                  (3)

Hence by summation, S_{n+1}-S_n = 0, proving (2) (modulo one initial
The rational function R(n,k) is called the _WZ_proof_certificate_. Its
knowledge makes a proof of (2)  available by verifying a single rational

8. Algorithm Hyper:
Petkovsek's algorithm is a decision procedure to determine all
hypergeometric term solutions of a given holonomic recurrence equation.
It uses a representation lemma for rational functions initially due to
Gosper, the _Gosper-Petkovsek_representation_, in a clever way.

III Epilogue

9. An operator algebra viewpoint:  The main theme of the book are
holonomic recurrence equations. Using the shift operator N a_n:=a_{n+1},
these can also be understood as operator equations, and one can deal with
them in a non-commutative algebra where the commutator rule Nn-nN=N is
valid.  In the given chapter this approach is considered in more detail.

In the Appendix the WWW sites and the software are discussed in more detail.

All algorithms that are discussed in the book under review are accompanied
by examples and a few exercises for the reader, some of which come with
solutions.  Furthermore, the authors give examples for the use of
Mathematica and Maple to do the computations.  It is assumed that the
reader has access to the World Wide Web or to other file transfer
services, as well as to either Maple or Mathematica since the use of
implementations of the algorithms considered seems to be a must.

The authors refer to Maple software available from Zeilberger's WWW site,
and to Mathematica software due to Krattenthaler (hypergeometric
database), Paule/Schorn (Gosper's and Zeilberger's algorithms) and
Petkovsek (Petkovsek's algorithm).  Implementational details are not
discussed.  Note that the Maple package 'sumtools' written by the reviewer
[2] comes with Maple V.4 and does also contain an implementation of both
Gosper's and Zeilberger's algorithms.

The presentation of the book is charming, and it gives an excellent
introduction to this modern topic. I would like to mention two minor
inconveniences, though.  First, the fact that the rational certificate of
an application of Zeilberger's algorithm might contain poles with some
obvious defects is not addressed. Second, I find it a little inconvenient
that in some instances the authors use different notations at different
places of the book.  This might be influenced by the fact that the book
forms essentially a collection of previously published material [1], [4],
[5], [6], [7].

There is no need, e.g., for new notations for rising and falling
factorials different from the ones given on pages 39 and 149,
respectively, in the proof of the "Fundamental Theorem" on p. 66. In my
opinion, this causes confusion. Similarly, the footnote on p. 157 about
the rising factorial notation is unnecessary since this definition is
given on p. 39. Even worse, the mentioned footnote contains a _wrong_

The authors mention the continuous analogues of the algorithms presented
without giving the details. A forthcoming book by the reviewer [3]
emphasizing the use of Maple for orthogonal polynomials and special
functions will cover these topics.

One of the highlights of the presentation is the consideration of finite
sums of hypergeometric terms. The authors show how Gosper's algorithm can
be extended to this case. This previously unnoticed fact is rather
important since summation is a linear operation, but Gosper's original
algorithm is not.


[1] Gessel, I.M.: Finding identities with the WZ method.
J. Symbolic Computation 20, 1995, 537--566.

[2] Koepf, Wolfram: Summation in Maple. Maple Technical Newsletter 3 (2),
1996, 26--32.

[3] Koepf, Wolfram: Hypergeometric Summation.  An Algorithmic Approach to
Hypergeometric Summation and Special Function Identities. Vieweg,
Braunschweig/Wiesbaden, 1997, to appear.

[4] Petkovsek, M.:  Hypergeometric solutions of linear recurrences with
polynomial coefficients.  J. Symbolic Comp. 14, 1992, 243--264.

[5] Wilf, H.S.:  Identities and their computer proofs. "SPICE" Lecture
Notes, 31 August - 2 September 1993.  Previously available by anonymous
ftp from ftp.cis.upenn.edu .

[6] Zeilberger, D.:  A fast algorithm for proving terminating
hypergeometric identities.  Discrete Math. 80, 1990, 207--211.

[7] Zeilberger, D.:  Three recitations on holonomic systems and
hypergeometric series.  J. Symbolic Computation 20, 1995, 699--724.

Wolfram Koepf

Topic #15  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Axel Riese <ariese@risc.uni-linz.ac.at>
Subject: q-Zeilberger algorithm in Mathematica updated

Dear q-experts !

I would like to inform you that a new version (1.8) of my Mathematica
implementation of the q-Zeilberger algorithm is available.

Besides several new features, the program is now MUCH faster than previous
versions. For instance, the rhs of identity (III.25) in the "Basic
Hypergeometric Series" book by G.Gasper and M.Rahman, a _{12} \phi _{11}
series leading to a recurrence of order 3, can be solved now in less than
1 minute on a Pentium 100.

The package is accompanied by a Mathematica 3.0 notebook consisting of about
500 examples.

I you are interested in obtaining the update, please let me know whether you
prefer receiving

- the file qZeil.tar.gz.uue (provided that you have tar, gzip and uudecode) or
- seven separate ASCII-files

by email.

Axel Riese

Topic #16  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: OP-SF NET Editor <thk@wins.uva.nl>
Subject: PhD project on History of Orthogonal Polynomials

I found the following announcement of a PhD project at URL's

At this moment 7 PhD and 1 Bursary positions are available at the Research
Institute of Mathematics and Computing Science (IWI) of the
University of Groningen (Netherlands).
Positions could be obtained in several specified research areas, one
of which is the following:

`The history of orthogonal polynomials'
Project leaders: Aad Dijksma and
Jan van Maanen (contact person, e-mail J.A.van.Maanen@math.rug.nl )

The aim of the project is to investigate various aspects of the historical
development of orthogonal polynomials (OP). The following aspects will be
taken into account:

     the chronology starts at about 1750, with the competitive work of
     Laplace and Legendre as a first major event
     already the fact that most of the special functions bear the names of
     mathematicians suggests the relevance of the biographical aspect.
     Competition and collaboration will be topics to focus at.
     the origin of several of these functions is closely linked to
     applications, ranging from probablity theory to potential theory.
changing roles
     from functions with interesting properties with respect to integration
     the orthogonal functions became elements in an vectorspace with inner
     product. This also changed the way in which mathematicians could `play'
     with them.

The objective is to write a `Microstoria'. The Microstoria-method takes a
restricted and clearly recognizable subject as a starting point and uses it
as a kernel for writing more general history. The timespan of the subject
(1750-1950), the involvement of several major mathematicians, the regular
use of OP in applied situations, the tendency to unify the theory of OP and
to cover the individual polynomials under a common heading, the handbook
tradition, are themes which, in combination with eachother, will lead to a
fresh description of the history of modern mathematics. Up to now there have
been partial studies in this field (e.g. by Szego (1958), Askey (1988), and
Meijer(1996)), but an overview is lacking. To produce such an overview,
which at the same time will be a `Microstoria' about mathematics in general,
is the central aim of the project.

Topic #17  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Doron Zeilberger
Subject: Don't Stop the Problems

Dear SIAM Officers,
Below is the lastest opinion in the Opinion column of my website.
I hope that you will reconsider getting rid of your problems.

Opinion #19 of Doron Zeilberger
SIAM Review Should Not Cancel its Problem Section

Written: Oct. 23, 1997

Cecil Rousseau, the problem editor of SIAM Review, has just told me that
SIAM Review's problem section's days are numbered.  I was shocked, but not
surprised.  I have already had a premonition of that, a few months ago,
when I read in SIAM News that SIAM Review is about to get a 'face lift'
and a 'new image'. I am always wary of such proposed improvements that
contribute to the contemporary trend to sacrifice content in favor of
fluff and 'image'. It is regrettable that even scientists, and
mathematicians to boot, have caught the image-obsession that has turned
politicians into puppets in the hands of sleazy PR-professionals.

The most interesting parts of the American Mathematical Monthly and SIAM
Review are their problem sections. Nobody reads the articles, but many
readers go straight to the problem section.  Almost as interesting as the
problems are the solutions.  One of my favorite books is Klamkin's
collection of problems from SIAM Reviews. Even from the snobbish,
prestige-hungry, point of view of the SIAM administration, there is
justification for the problem section. For example, Mehta's famous
integral (that turned out to follow from Selberg's once-dormant 1944
paper), made its first appearance as a problem in SIAM Review. Similar
things can be said about Monthly problems, for example, Erdos's problem
from 1946 that started Euclidean Ramsey theory, and the famous
Busseman-Petit conjecture that was first raised as a Monthly problem.

But, most importantly, Problem sections turned many young people into
mathematicians. It was the late Joe Gillis's 'Gilyonot leMatematika' (and
that hopefully still exists today), and especially its problem section,
that made me, and many of my friends in Israel, into mathematicians.

I also feel a personal loss. My first 'publication', in 1970, when I was
an undergrad, was a solved problem in SIAM Review.  Both the problem and
my solution were real gems.  I'll forget my right hand before I'll forget
it. Let G be a finite group with n elements, and let S be any subset.
Prove that S^n is a subgroup. My solution went as follows.  When |S|=1 it
is trivial. Otherwise, by pigeon-hole, there must be an i such that
|S^(i)|=|S^(i+1)|, hence S^(i+1)=aS^i, for some a in G, and hence
S^n=a^(n-i)S^i, S^(2n)=a^(2n-i)S^i=a^n S^n=S^n, hence (S^n)^2=S^n and S^n
is a subgroup.  I was so proud and delighted when I first solved it, and
was really ecstatic when Murray Klamkin decided to publish my solution.  I
am sure that many had a similar experience.

In conclusion, let me quote Herb Wilf, who in a recent bio in the Monthly
wrote (AMM 104 no. 6 (June-July 1997), p. 588):  'Herbert Wilf has been
editor of this Monthly, and remembers well how the 'Problems and
Solutions' tail often wagged the Monthly dog'. The same is true of SIAM
Review, and it is a very stupid dog-owner that chops his dog's tail,
especially one that wags so well.

Doron Zeilberger

Topic #18  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: OP-SF Editors <tkh@wins.uva.nl> <muldoon@yorku.ca>
Subject: Further comments on SIAM Review Problem Section

Doron Zeilberger's Web Site provides further comments on his opinion
(Topic #16) concerning the SIAM Review Problem Section. The following is
taken from the URL: http://www.math.temple.edu/~zeilberg/res19 .

Richard Askey <askey@math.wisc.edu>:
  Let me second Doron Zeilberger's comments about the Problem Section in
SIAM Review.  He is wrong about Mehta's problem first appearing in SIAM
Review's Problem Section, since it had appeared in a joint paper with
Freeman Dyson.  However, no one could solve it and it was completely
missed by mathematicians in their paper in J. Math. Physics, so it was
important to have it appear in SIAM Review to bring it to the attention of
mathematicians who might have been able to solve it.  Eventually, a direct
evaluation of this integral was found which did not have to go to the more
general integral of Selberg.  The argument used to evaluate this integral
directly was also used to evaluate some finite sums of real interest and
the argument found by Selberg and a later argument of Aomoto, which
appeared in SIAM J Math Anal do not work in the finite character sum case.
    Cecil Rousseau had sent me Mehta's problem to referee for SIAM Review,
and I spent a fair amount of time trying to solve it.  If I had not, it is
not clear that I would have appreciated Selberg's integral as I did, and
found some conjectured extensions of it.  These were published in SIAM
Jour.  Math. Anal., and eventually proven.  Thus a problem in a problem
section can be useful even if no one is able to solve it because of its
publication in a problem section.
    Doron's point about young people being attracted to a subject by
problems they can work on is important.  It might be useful for SIAM to
set up a student problem section.  I hope that the problems were not
dropped because they do not correspond to the type of problem which the
officers think arises in applied mathematics, for I can assure them that
many of the problems involving special functions which have appeared in
SIAM Review are similar to those that are sent to me by mathematicians and
others who come across them in their applied work.  Just today, someone
was here to talk about inverse problems, and Lommel polynomials arose in a
very natural way.  Their orthogonality relation may be important in trying
to solve the original inverse problem.  The orthogonality appeared in a
paper in Proc. Amer. Math. Soc., but it easily could have been a problem
in SIAM Review.
    I do not agree with all of the arguments given by Zeilberger about why
this problem section was stopped, but agree with him that this is

Jonathan Borwein <jborwein@cecm.sfu.ca>:
I would like to echo Doron Zeilberger's strong support for the SIAM
problem section. Pleas also remember that many more people look at and
discuss these problems than submit solutions.

N. J. A. Sloane <njas@research.att.com>:
I completely agree with Doron.

Andrew Granville <andrew@sophie.math.uga.edu>:
Good; I'm glad that you are after them on this.  Just because the editors
now wear long trousers, it doesn't mean there aren't short trousered kids
coming along who can't benefit from the fun of solving problems.

Andrew Odlyzko <amo@research.att.com>:
I agree completely with your opinion.

Peter Paule <Peter.Paule@risc.uni-linz.ac.at>:
I am writing in order to fully support Doron Zeilberger's "Opinion 19" -
"SIAM Review Should Not Cancel its Problem Section".

Topic #19  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Mary Rose Mucci, Journals Publisher, SIAM <muccie@siam.org>
Subject: Problems and Solutions Section

     SIAM would like to thank the members of the Orthogonal Polynomials
     and Special Functions activity group for their interest in and support of
     Problems and Solutions.  We are happy to know that you have such a
     high regard for the section and would like to take this opportunity
     to clarify SIAM's plans for the future of Problems and Solutions.

     While it is true that the Problems and Solutions will no longer be
     included as part of SIAM Review, the section has not been eliminated.
     Because of its format and audience, SIAM has designated Problems and
     Solutions as its first electronic-only publication.  Problems and
     Solutions will continue on the World Wide Web in 1999 and beyond.

     Many of you have pointed out that the Problems and Solutions are
     particularly useful to students and younger researchers and may help
     to entice young people to become mathematicians.  We believe that an
     electronic format will appeal to these younger researchers and
     entice them to solve the problems and submit their solutions.  We
     also hope that the wide readership possible with a free, web-based
     publication will bring the Problems and Solutions to the attention of
     students, researchers, and other interested parties  who may not have
     had the opportunity to read the section in SIAM Review.

     The Problems and Solutions will be available freely to everyone. They
     will not be part of SIAM Journals Online, which cannot be accessed
     without a subscription.

     For the immediate future, we anticipate the submission and review
     procedures for Problems and Solutions to continue as they are now.
     The editor(s) will continue to take submissions of both problems and
     solutions, choose the best ones, and send them to SIAM.   SIAM will
     publish the Problems and Solutions individually on the web in PDF
     format with an HTML table of contents listing the titles and authors.
     Therefore readers will be able to click on the title of the problem
     or solution that interests them and go right to it.  We will also print
     the names of the problem proposers and solvers regularly in a SIAM
     publication.  SIAM News or the Education section of SIAM Review have
     been suggested as appropriate places to publish them.

     There are many things we would like to do with the electronic
     Problems and Solutions section in the future, such as allowing people to
     submit both problems and solutions electronically via the web and linking
     to related material.  But given SIAM's current capabilities and the
     existing electronic publishing system, our initial proposal is fairly
     straightforward.  We know that we can follow the procedures  outlined
     above with our current electronic publishing setup.  As that evolves
     we may be able to expand and update the way the Problems and
     Solutions section works.

     The Orthogonal Polynomials and Special Functions Activity Group has
     been steadfast in its support of Problems and Solutions.  We would be
     pleased if the activity group became involved in the electronic
     version. I encourage you to contact me directly if you have ideas for
     possible involvement, additional comments, or questions about what is
     outlined above.  Thank you again for your support of Problems and

     Mary Rose Muccie
     Journals Publisher, SIAM

Topic #20  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Bill Gosper <rwg@NEWTON.macsyma.com>
Subject: Lambert-W function and OPSF Flamesite?

Editor's note: Readers of OP-SF net may be interested in reading
the following messages by Bill Gosper, addressed to Hans Haubold,
but with cc to several others including Tom Koornwinder.

> From rwg@SWEATHOUSE.macsyma.com Sun Sep 28 22:24 MET 1997
> To: haubold@Mail.Austria.EU.net

Prof Haubold,

Thank you for the OPSF-FTPSITE notice.  Can you suggest a site or list to
which I could submit for informal discussion a proposal that the so-called
Lambert-W function be de-popularized in favor of the (unnamed?) function
which inverts x exp(x^2) instead of x exp(x)?  The name-needing function
has equally nice series and asymptotics, and far nicer branch structure.
Tnx again,
   -- Bill Gosper

> From rwg@SWEATHOUSE.macsyma.com Fri Oct  3 02:08 MET 1997
> To: haubold@Mail.Austria.EU.net

Dear Professors Haubold & Koornwinder,

I found only one mathematical item among the five 1997 Bulletins;
and the Newsletter turnaround is too slow.

HJH>Thank you for your e-mail of 28 September 1997 regarding a site or
    list to discuss the naming of "useful functions". There are papers in
    the history of physics/mathematics dealing with that issue but there
    is no site or list on the WWW for informal discussions on that.

Pity.  I was hoping to hear from someone that, e.g., "Joe Blowinder
studied the inversion of x*exp(x^2) in 1869", so we could name it
Blowinder's function.

But naming it is only half the problem.  The special functions world is
beginning to embrace what seems to me a much inferior alternative-- the
so-called Lambert W function, and I want to offer, side by side, their
respective series, asymptotics, integrals, derivatives, and, most of all,
symmetries (or lack thereof).  It's sort of like trying to avert the
headaches caused by initially defining Bernoulli numbers to have all
positive signs, and no intervening zeros.

Another use for electronically quick turnaround is for tidbits and
questions of the form "Hey, is this new?".  E.g.,

> Date: Wed, 1 Oct 1997 18:01 EDT
> From: rwg@SWEATHOUSE.macsyma.com

[Attn:  Eric Weisstein]
At least for integer h, you can expand

            (j + h)!   \                            k - 1
            -------- =  >    Stirling_s1(h + 1, k) j
               j!      /

which, if you divide by h!, expands the binomial coefficient, and can be
regarded as a definition of Stirling (cycle) numbers for noninteger h.
But then we lose termination and run into convergence problems, and seek
an asymptotic expansion.

In Eric's trove (http://www.astro.virginia.edu/~eww6n/math/), under Gamma
Function, applications of Stirling's expansion, he derives

Gamma(j+1/2)/Gamma(j) ~ sqrt(j) (1 - 1/(24 j^2) + 1/(48 j^3) + ...).

It appears that

          (j + h)!   \     Stirling_s1(h + 1, - k + h + 1)
(*)       -------- =  >    -------------------------------,
             j!      /                  k - h
                     ====              j

or, for you troglodyte Gammaphiles,

 Gamma(j + h)   \     Stirling_s1(h, h - k)
 ------------ =  >    --------------------- =
   Gamma(j)     /             k - h
                ====         j
                k = 0

   h       (h - 1) h   (h - 2) (3 h - 1) (h - 1) h
  j   (1 + --------- + ---------------------------
              2 j                     2
                                  24 j

                           2  2
    (h - 3) (h - 2) (h - 1)  h
  + ---------------------------
               48 j

                 3       2
    (h - 4) (15 h  - 30 h  + 5 h + 2) (h - 3) (h - 2) (h - 1) h
  + -----------------------------------------------------------
                              5760 j

                2                                           2  2
    (h - 5) (3 h  - 7 h - 2) (h - 4) (h - 3) (h - 2) (h - 1)  h
  + ------------------------------------------------------------
                              11520 j

  + . . .),

(which requires no noninteger Stirling theology).

For h=1/2, this gives

  Gamma(j + -)
  ------------ = sqrt(j)

              1      1         5         21         399
        (1 - --- + ------ + ------- - -------- - --------- + . . . ),
             8 j        2         3          4           5
                   128 j    1024 j    32768 j    262144 j

so we disagree.

Does anyone remember seeing (*) before?  It looks pretty useful, but I
can't find it in G, Knuth, & P.  We might regard Gamma(j+h)/Gamma(j)
as the generating function for the "unreduced Stirling polynomials".
My guess is that a place for such things is already growing in the
vast unruliness of the Web.

But thanks for your suggestions.   --Bill Gosper

Topic #21  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: A. Bogardo <bogardo@siam.org>
Subject: SIAM Student Paper Prizes

                       SIAM Student Paper Prizes

 The annual SIAM Student Paper Prizes will be awarded during the
 1998 SIAM Annual Meeting, July 13-17, at the University of Toronto.

 If you are a student or know of a student who would like to take
 part in the competition, here are the details:

 The authors of the three best papers in applied and computational
 mathematics written by students and submitted to SIAM will present
 their papers at the meeting and will receive a $750 cash prize as
 well as gratis registration for the meeting.  The winners will be
 awarded calligraphed certificates at a special prize ceremony at
 the meeting.  Papers must be singly authored and not previously
 published or submitted for publication to be eligible for
 consideration.  To qualify, authors must be students in good
 standing who have not received their PhDs at the time of

 In submitting their work for publication, authors are asked to
 consider SIAM journals.  However, student paper prize winners are
 not guaranteed publication in any SIAM journal; all papers
 submitted to SIAM journals are subject to the same refereeing
 process and standards.

 Submissions must be received in the SIAM office on or before
 March 15, 1998.

 Submissions, which must be in English, can be sent by regular mail
 or fax.  Each submission must include (1) an extended abstract NOT
 LONGER THAN 5 PAGES (including bibliography); (2) the complete
 paper, which will be used solely for clarification of any
 questions; (3) a statement by the student's faculty advisor that
 the paper has been prepared by the author indicated and that the
 author is a student in good standing; (4) a letter by the student's
 faculty advisor describing and evaluating the paper's contribution;
 and (5) a short biography of the student.

 Submissions will be judged on originality, significance, and
 quality of exposition.

 The winners will be notified by June 1, 1998.

 Please direct your submission and any questions you may have to
 A. Bogardo at SIAM, 3600 University City Science Center,
 Philadelphia, PA 19104-2688;telephone (215) 382-9800; e-mail to
 bogardo@siam.org; fax to (215) 386-7999.

Topic #22  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: A. Bogardo <bogardo@siam.org>
Subject: SIAM Student Travel Awards

                          SIAM Student Travel Awards
                      SIAM Conferences and Annual Meeting

     During 1998, SIAM will make a number of awards for $300 to
     support student travel to each of the following SIAM conferences:

        Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
        January 25-27, San Francisco, CA

        Fourth SIAM Conference on Control and Its Applications
        May 7-9, Jacksonville, FL

        Fourth International Conference on Mathematical and
           Numerical Aspects of Wave Propagation
        June 1-5, Golden, CO

        Ninth SIAM Conference on Discrete Mathematics
        July 12-15, Toronto, CANADA

        SIAM Annual Meeting
        July 13-17, Toronto, CANADA

        Industrial Workshop on Computer-Aided Design
          and Manufacturing
        October 22-23, Troy, MI

     The awards are to be made from the SIAM Student Travel Fund,
     created in 1991 and maintained through book royalties
     donated by generous SIAM authors.

     Any full-time student in good standing is eligible to
     receive an award plus gratis meeting registration.  Top
     priority will be given to students presenting papers at the
     meeting, with second priority to students who are co-authors
     of papers to be presented at the meetings.  Only students
     traveling more than 100 miles to the meetings are eligible
     for the awards.

     An application for a travel award must include:

        (1) A letter from the student describing his/her
            academic standing and interests, his/her expected
            graduation date and degree, advisor's name,
            and, if available, a URL for a working Web

        (2) A one-page vita that includes the student's
            research interests, projects, and papers

        (3) A detailed letter from the student's faculty
            advisor indicating why the student is deserving
            of receiving a travel award and any special circumstances.

        (4) If applicable, the title(s) of the paper(s) to be
            presented (co-authored) by the student at the

     Applications should be sent to the SIAM office (Attention:
     SIAM Student Travel Awards), 3600 University City Science
     Center, Philadelphia, PA 19104-2688.  Students also may
     apply by e-mail to bogardo@siam.org or by fax to 215-386-7999.

     Complete applications must be received at the SIAM office no
     later than TWO MONTHS before the first day of the meeting for
     which support is requested.

     Winners will be notified FIVE WEEKS before the first day of the
     meeting. Checks for the awards will be given to the winning
     students when they arrive at the given meeting and check in at
     the SIAM Registration Desk.

Topic #23  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: A. Bogardo <bogardo@siam.org>
Subject: W. T. and Idalia Reid Prize

                             CALL FOR NOMINATIONS
                          W.T. and IDALIA REID PRIZE

     The Reid Prize

     SIAM will present the W.T. and Idalia Reid Prize at the 1998 SIAM
     Annual Meeting in Toronto, Canada, July 13-17.  The award will be
     given for research in, or other contributions to, the broadly
     defined areas of differential equations and control theory.  The
     prize may be given either for a single notable achievement or for a
     collection of such achievements.


     The prize is awarded to any member of the scientific community who
     meets the general guidelines of the prize description above.

     Description of Award

     The award consists of an engraved medal and a $10,000 cash prize.


     A letter of nomination, including a description of achievement(s)
     should be sent by February 1, 1998 to:

                Professor John A. Burns
                Chair, Reid Prize Selection Committee
                c/o Allison Bogardo
                3600 University City Science Center
                Philadelphia, PA 19104-2688
                Telephone: (215) 382-9800
                Fax:       (215) 386-7999
                E-mail:    bogardo@siam.org

Topic #24  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Hans Haubold <haubold@Mail.Austria.EU.net> and
      OP-SF NET editor <thk@wins.uva.nl>
Subject: preprint archive for papers in Orthogonal Polynomials and Special

Hans Haubold's ftp archive for preprints in the area of Orthogonal
Polynomials and Special functions is the continuation of Waleed Al-Salam's
preprint archive. It can be approached via a home page:


This home page links to pages
- Index by Author (with links to the actual manuscript files)
- Abstracts listed by Author(s) (mostly with abstracts of papers for which
   the full manuscript file resides elsewhere; hyperlinks are provided)
- Submission form

You can also move from the home page to the ftp interface and to the the
submissions directory, where the most recent contributions reside.

Of course, you can also download or upload by anonymous ftp. Connect with:
unvie6.un.or.at, directory siam.

Submission of manuscripts:

You are invited to submit one or more of your not-yet-in-print
manuscripts which you wish to make available to the OPSF Activity
Group. They should be prepared in TeX, LaTeX, AMSTeX, AMSLaTeX,
or PS format.

Suggestion A:

1. Please complete the
submission form

2. Log into the anonymous ftp site "unvie6.un.or.at"

3. Upload your file(s) into the directory

4. Eventually your file(s) will be transferred to the directory
"siam/opsf_new" in due time.

Suggestion B:

1. Please complete the
submission form

2. Send your file(s) by e-mail to

3. Your file(s) will be transferred to the directory

4. Eventually your file(s) will be transferred to the directory
"siam/opsf_new" in due time.

There are two new features in connection with submitting manuscripts
to the ftp site:

- If you submit a file with a full manuscript, it is recommended (though
  not obligatory) to also supply an abstract file (plain ASCII text, no

- It is also possible to submit only an abstract file together with a
  hyperlink to the actual full manuscript. In this case, please supply
  the hyperlink in the "Comments" Text-Area, when filling out the
  submission form.

Recent submissions:

G. Bangerezako, Discrete Darboux transformation for discrete
polynomials of hypergeometric type

I. V. Krasovsky, Asymptotic distance between zeros of orthogonal
satisfying second-order differential equations

W. Lang, On sums of powers of zeros of polynomials

Topic #25  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: OP-SF NET Editors <thk@wins.uva.nl>, <muldoon@yorku.ca>
Subject: Changes of Address, WWW Pages, etc.

As of September 1, 1997, Wolfram Koepf was appointed Professor of Applied
Mathematics at the Hochschule fur Technik, Wirtschaft und Kultur Leipzig,
Germany, Department of Computer Science, Mathematics and Natural Sciences
(Informatik, Mathematik und Naturwissenschaften). His new address there
Prof. Dr. Wolfram Koepf
Fachbereich IMN
HTWK Leipzig
Gustav-Freytag-Str. 42 A
D-04277 Leipzig
phone: +49-341-307 64 95
fax: +49-341-301 27 22
e-mail: koepf@imn.htwk-leipzig.de
WWW: http://www.imn.htwk-leipzig.de/~koepf

For a few months, however, he will be still affiliated with
Konrad-Zuse-Zentrum so his old e-mail address and home page will still be

Semyon Yakubovich will be returning to Minsk (from Leuven) at the end of
1997.  His address there will be:

Dr. S.B.Yakubovich
P.O.Box 385

Here are some recent additions to our list of home pages:

Maple package for symmetric functions (John Stembridge) at URL:

NAVIMA: Namur-Vigo-Madrid, Group on Connection and Linearization Problems
has a URL:

SCAGOP: Spanish Computer Algebra Group on Orthogonal Polynomials
has moved to URL:

Roelof Koekoek at Technical University Delft has a home page:

Willard Miller, Director of
Institute for Mathematics and its Applications,
University of Minnesota has a home page:

Margit Roesler has a home page at:

Vadim Zelenkov <zelenkov@gray.isir.minsk.by> thanks all those who have
sent their abstracts, papers, links, etc. in connection with the
Krawtchouk Polynomials Home Page (OP-SF NET 4.5, Topic #14). The first
draft is on the Web at the URL:


All proposals, additions, corrections will be appreciated.

Topic #26  ------------   OP-SF NET 4.6  ------------ November 15, 1997
-From: OP-SF NET Editor <thk@wins.uva.nl>
-Subject: Alternative way to subscribe to OP-SF NET
-From now on there will be two ways to subscribe to OP-SF NET:

1. Send a message to


with your name and email address in the body of the message. If
everything works well, you will be put on the mailing list of
OP-SF NET which is maintained by SIAM.

2. Send a message to


and put in the body of the message as only words:

     subscribe opsfnet

This is handled by an automatic list server. You will receive a confirmation,
with a list of further commands. You will be put on the opsfnet
mailing list of this list server. A new issue of OP-SF NET will be mailed
to people on this list  immediately after the mailing by SIAM to the people
on the list maintained by SIAM.

Topic #27  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: OP-SF NET Editor <thk@wins.uva.nl>
Subject: Starting a new listserv for discussions on OP & SF

The listserv discussed in OP-SF NET 4.4, Topic #8, will start on
Monday, November 24.
Quoting from OP-SF NET 4.4, Topic #8:

"It has been suggested that an OPSF listserv should be started. Such a
listserv could be useful in promoting discussion and posing questions in
the general areas of orthogonal polynomials and special functions. A
selection of contributions could be included in OP-SF NET. It has been
suggested that we might create an automatic way to subscribe and
unsubscribe to the listserv and OP-SF NET. To make it workable, the
listserv would probably have to be "unmoderated" which means that the
Group would have no control over what might appear there. Some have
observed that this could lead to abuse.  In any case, such a listserv
need not have any official connection to our Activity Group, though it
could be publicized in the Group's media."

A listserv as described above will be started now.  It will be
maintained by Tom Koornwinder.  It will be unmoderated. However, in
case of (repeated) abuse, it will be transformed into a moderated listserv.
Starting November 24, you can act as follows.
For subscribing, send a message to


and put in the body of the message as only words:

     subscribe opsftalk

You can post messages by sending mail to


Your message will then be automatically forwarded to everybody
on the opsftalk list.

Topic #28  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: OP-SF NET Editors <thk@wins.uva.nl>, <muldoon@yorku.ca>
Subject: Obtaining back issues of OP-SF NET and submitting contributions
         to OP-SF NET and Newsletter

Back issues of OP-SF NET can be obtained from
     ftp:     ftp.wins.uva.nl, in directory
or   WWW:     http://turing.wins.uva.nl/~thk/opsfnet/

or   WWW: http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html

Contributions to the OP-SF NET 5.1 should reach the email address
poly@siam.org before January 1, 1998.

The Activity Group also sponsors a (printed) Newsletter edited by Wolfram
Koepf. Deadline for submissions to be included in the February 1998 issue
is January 15, 1998.

Please send your Newsletter contributions directly to the Editor:

Wolfram Koepf
Fachbereich IMN
HTWK Leipzig
Gustav-Freytag-Str. 42 A
D-04277 Leipzig
phone: +49-341-307 64 95
fax: +49-341-301 27 22
e-mail: koepf@imn.htwk-leipzig.de

preferably by email, and in latex format. Other formats are also
acceptable and can be submitted by email, regular mail or fax.

Please note that submissions to the Newsletter (if not containing
mathematics symbols or pictures) are automatically considered for
publication in OP-SF NET, and vice versa, unless the writer requests

Previous issues of the Newsletter, but not the most recent one, can
be obtained as dvi or PostScript files from Wolfram Koepf's WWW homepage:


or by anonymous ftp at

   ftp.zib.de   in directory   pub/UserHome/Koepf/SIAM

In order to join the SIAM Activity Group on Orthogonal Polynomials
and Special Functions, and thereby receive the Newsletter,
you have to become a member of SIAM. The annual dues are $93 for
SIAM plus $10 for the Group. Student memberships are $20 a year
with free membership in one Activity Group. Postgraduates can join
for $45 a year (for three years). Contact the email address join@siam.org

o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o
-  OP-SF NET is a forum of the SIAM Activity Group on                 -
-  Special Functions and Orthogonal Polynomials.                      -
-  We disseminate your contributions on anything of interest to the   -
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