Volume 3, Number 6

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-                                                                     -
-                                           November 15, 1996         -
-      O P - S F   N E T                    Volume 3, 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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Today's Topics:
     1. Editorship, SIAM J. Math. Anal.
     2. History of OP & SF on OP-SF WEB
     3. Revising the 1991 Mathematics Subject Classification
     4. SIAM Student Paper Prizes
     5. One-day meeting in Leuven on Constructive Complex Analysis
     6. Centenary conference at Univ. of Wisconsin - Madison
     7. Death of Felix Arscott
     8. Postdoctoral Opportunity in Computation of Special Functions
     9. Report of Madrid Workshop on Orthogonal Polynomials in
         Mathematical Physics
    10. Bibliography on Orthogonal Polynomials
    11. Extended version of Askey-Wilson-scheme report
    12. Review of "Table of Integrals, Series, and Products,
         CD-ROM Version 1.0"
    13. Book announcement on Quantum Theory of Angular Momentum
    14. Announcement of edited book on Symmetries and Integrability of
         Difference Equations
    15. Mathai Festschrift
    16. Announcement of book on Zonal Polynomials
    17. Announcement of edited book on Mathematical Analysis, Wavelets and
         Signal Processing
    18. Announcement of book on Polynomials and Polynomial Inequalities
    19. The Collected Works of Lars Onsager
    20. ftp site for papers in Orthogonal Polynomials and Special
    21. Changes of Address, WWW pages. etc.
    22. Part 33 of 1991 Mathematics Subject Classification
    23. Montreal Workshop on Calogero-Moser-Sutherland systems
    24. Obtaining back issues of OP-SF Net and submitting contributions
         to OP-SF Net and Newsletter

Calendar of events:                                         see issue/topic:

November 28: One-day meeting in Leuven on Constructive Complex Analysis
                                                                    3.6 #5

January 13-24: Workshop on Special Functions & Differential
      Equations, Madras                                             3.3 #6
March 10-15: Workshop on Calogero-Moser-Sutherland Systems
        in Montreal                                                3.6 #23
March 17 - May 30: MSRI program on Symmetric functions and
        representation theory                                       3.3 #5
May 22-24: Centenary Conference, including minisymposium on special
    functions in Madison, Wisconsin                                 3.4 #5
June 2-6: First ISAAC Conference (International Society for Analysis,
    its  Applications and Computation) in Newark, Delaware          3.5 #3
June 9-20: CRM Workshop on Algebraic Combinatorics, Montreal        3.5 #4
June 24-28: Continued Fractions and Geometric Function Theory
            (Trondheim, Norway)                                     3.2 #8
July 14-18: SIAM 45th Anniversary Meeting, Stanford, California
July 14-18: 9th International Conference on Formal Power Series
  and Algebraic Combinatorics, Vienna, Austria                      3.4 #7
September 22-26: VIII Simposium sobre Polinomios Ortogonales y
   Aplicaciones, Seville, Spain                                     3.5 #5

Topic #1  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Nico Temme <nicot@cwi.nl>
Subject: Editorship, SIAM J. Math. Anal.

I want to inform the OP & SF community that I have accepted an invitation
from Managing Editor DiBenedetto to join the editorial board of SIAM J.
Math. Analysis.

I have pointed out that my main activities are in asymptotics (also
related with special functions) and that I expect that more theoretical
papers on special functions and orthogonal polynomials will be handled by
a different editor.

Nico Temme

Topic #2  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Tom Koornwinder <thk@wins.uva.nl>
Subject: History of OP & SF on OP-SF WEB

On OP-SF WEB we have started a page about the history of OP & SF; see


This section of OP-SF WEB is intended to provide on-line information on
significant contributors to Orthogonal Polynomials and Special Functions,
who are no longer alive.  A rich source of initial information can be
found in the History of Mathematics archive at St. Andrews University, see


In particular, consult their full alphabetical index and their search
form.  A quick scan revealed the names of

Airy, Akhiezer, Appell, Bateman, Bell, Bessel, Catalan, Chebyshev,
Chandrasekhar, Coulomb, Dixon, Erdelyi, Euler, Fibonacci, Gauss,
Gegenbauer, Henrici, Jacobi, Kummer, Laguerre, Legendre, Lerch,
Mascheroni, Pade, Pfaff, Ramanujan, Stieltjes, Sturm, Szego, Ulam,
Vandermonde, Whittaker.

Probably, many further names relevant for our field can be found there.

On our Web page we will provide specific links to places elsewhere on the
Web which provide historical information about persons significant for our
field. Until now we only know about a few such places.  We invite our
readers to inform us about other relevant places.  We also want to ask you
to write a page about your favourite mathematician from history if you
think that this person is not yet sufficiently covered on the Web.

Topic #3  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Tom Koornwinder <thk@wins.uva.nl>
Subject: Revising the 1991 Mathematics Subject Classification

In OP-SF Net 3.3, topic #12, we printed the following information which
was taken from Notices AMS, December 1995, p.1547, see also
WWW: http://www.ams.org/committee/publications/msc-2000-let.html

> Mathematics Subject Classification Scheme Revision
> To the Mathematical Community:
> The editors of Mathematical Reviews and Zentralblatt fur Mathematik
> have initiated the process of revising the 1991 Mathematics Subject
> Classification, which is used by both journals as their classification
> system. The editors do not plan a radical revision of the present 1991
> system, but it is clear that some changes will be needed in order to
> accommodate recent developments in mathematical research.
> It will be necessary to have this revision completed by the end of 1998
> so that it can begin to be used in Current Mathematical Publications in
> mid 1999, and in Mathematical Reviews and Zentralblatt fur Mathematik
> beginning in 2000.
> We hereby solicit comments and suggestions from the mathematical
> community to be considered in this revision process. These should be
> submitted by June, 1997. The preferred method of communication is by
> e-mail:
> msc2000@ams.org or msc2000@zblmath.fiz-karlsruhe.de
> (Comments and suggestions may also be sent to either one of us at the
> addresses given below.)  We are eager that research mathematicians and
> scholars have input in this revision process as soon as possible.
>    R. Keith Dennis                    Bernd Wegner
>    Executive Editor                   Chefredakteur
>    Mathematical Reviews               Zentralblatt fur Mathematik

We called then for suggestions for revision concerning the sections on
Orthogonal Polynomials and Special Functions. (For your convenience we
have included part 33 of the 1991 Math. Subject Classification as Topic
#22 near the end of this issue.)  Up to now we have received the following

Wolfram Koepf <koepf@zib.de>:
- In one way or the other the Askey-Wilson scheme should appear here.
  One could mention these in 33C45 and 33D45. A distinction between these
  "classical" systems and other systems could also be helpful.
- Algorithmic methods, and/or the use of symbolic computation could be
  mentioned explicitly.

Charles Dunkl <cfd5z@virginia.edu>:
- Should wavelets get more attention in 42c?
- A finer classification of Askey-Wilson types?
- A cross-reference to quantum groups?

Tom Koornwinder <thk@wins.uva.nl>:
- 33C45, change into:
  Orthogonal polynomials and functions of hypergeometric type
  (Jacobi, Laguerre, Hermite, Askey scheme, etc.; see 42C05 for general
  orthogonal polynomials and functions)
- add: 33C47 Other special orthogonal polynomials and functions
- 33C50: change into:
  Orthogonal polynomials and functions in several variables expressible
  in terms of special functions in one variable
- add: 33C52 Special functions associated with root systems
- 33C55, change into: Spherical harmonics
  Motivation: ultraspherical polynomials unrelated to spherical harmonics
  are covered by 33C45; spherical functions (on Gelfand pairs) are covered
  by 33C80
- 33C80, change into: Connections with groups, algebras and related topics
- 33D10: What is the difference between theta functions and basic theta
- 33D15 and 33D20: What is the distinction between basic hypergeometric
  functions and generalized hypergeometric functions? For instance:
  the first category is r phi s with r<=2 and s<=1 and the second category
  is general r phi s ?
- 33D45, change into: Orthogonal polynomials and functions of
  q-hypergeometric type (Askey-Wilson polynomials, etc.)
- add: 33D50 Orthogonal polynomials and functions in several variables
  expressible in terms of q-special functions in one variable
- add: 33D52 q-Special functions associated with root systems
- 33D55: skip this item, it is not clear what is meant.
- 33C80, change into: Connections with quantum groups, Chevalley groups,
  p-adic groups, Hecke algebras and related topics
- 42C05. change into: Orthogonal functions and polynomials in one
  variable, general theory [See also ... ]
- add: 42C07: Orthogonal functions and polynomials in several variables,
  general theory [See also ... ]

Readers of OP-SF Net are invited to send us their comments for inclusion
in the next issue of OP-SF Net. All comments will be eventually bundled
and passed to the Executive Editor of Mathematical Reviews.

Topic #4  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Allison Bogardo <bogardo@siam.org>
Subject: SIAM Student Paper Prizes

The annual SIAM Student Paper Prizes will be awarded during the 1997 SIAM
Annual Meeting.

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 be invited to
attend the 1997 annual meeting in Stanford, California, July 14-18.  Each
winner must present his/her paper at the meeting and will receive a $750
cash award as well as gratis registration for the meeting.  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 submission.

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 by SIAM on or before March 15, 1997.

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

The winners will be notified by June 1, 1997.

If you have any questions, please contact 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 #5  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Walter Van Assche
Subject:  One-day meeting in Leuven on Constructive Complex Analysis

On Thursday, November 28, a one-day meeting will be organized at the
Katholieke Universiteit Leuven. The topic is

                   Constructive Complex Analysis.

Speakers are

* Arno Kuijlaars: "A survey of approximation, potential theory and
                   Chebyshev quadrature"
* Walter Van Assche: "An introduction to Hermite-Pade simultaneous rational
* Jeffrey S. Geronimo: "Orthogonal polynomials on the unit circle with random
                       recurrence coefficients"
* Valeri Kaliaguine: "Spectral theory for non-symmetric operators associated
                      with simultaneous rational approximation"
* Guillermo Lopez Lagomasino: "Orthogonal polynomials with complex
                               recurrence coefficients"

More information can be found at

Topic #6  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Charles Dunkl <cfd5z@virginia.edu>
Subject: Centenary conference at Univ. of Wisconsin - Madison

This conference, to be held on May 22-24, 1997, was announced in OP-SF Net
3.4, Topic #5.

Charles Dunkl will be organising a minisymposium there on special
functions. Participants will have to pay their own transportation, lodging
and meals, but there will be no registration fees. Anybody who would like
to be considered by Charles as a speaker at the special function session
should contact him as soon as possible, since he is forming the program by
the end of November.

Topic #7  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Martin Muldoon <muldoon@yorku.ca>
Subject: Death of Felix Arscott

Felix Arscott, Professor Emeritus in the Department of Applied Mathematics
at the University of Manitoba, died suddenly on July 5, 1996 while on
holiday in England.

Professor Arscott was a leading expert in the "higher special functions"
and associated differential equations (a paper of his from 1980 is
picturesquely titled "The Land beyond Bessel") and is one of the authors
of the recent monograph "Heun's Differential Equations", Oxford University
Press, 1995 (OP-SF NET 2-5, Topic #11).

Born in the London suburb of Greenwich in 1922, Professor Arscott spent
most of the Second World War in the Royal Air Force, leaving the service
as a commissioned officer and having gained an honours degree in
Mathematics from the University of London by private study. After a few
years of teaching, he completed an M.Sc. in Mathematics in 1951, and went
to teach mathematics at Makerere College, then the leading educational
institution in eastern Africa.  During this period, he wrote a thesis on
special functions and received the Ph.D. of the University of London in
1956.  There followed positions at Aberdeen, Battersea College of
Technology (later the University of Surrey) and the University of Reading.
During this period he coauthored with I. M. Khabaza the book "Tables of
Lame polynomials", Pergamon Press (1962), wrote "Periodic Differential
Equations:  An Introduction to Mathieu, Lame, and Allied Functions",
Pergamon (1964) and translated O. Boruvka's "Linear differential
transformations of the second order", English Universities Press (1971).
Along the way, he had been a visiting professor at the Universities of
Wisconsin and Calgary, had supervised six Ph.D. theses, had written 21
papers and was a founding Fellow of the Institute of Mathematics and its

In 1974, Arscott became Head of the fledgling Department of Applied
Mathematics at the University of Manitoba, a position he was to hold for
eleven years.  Apart from administrative leaves at Oxford and Dundee, he
was associated with the University of Manitoba for the rest of his life.
He accomplished much at Manitoba, building a Department which did all of
the Engineers' service teaching and set up Science programmes in Applied

Apart from the work mentioned above, Felix Arscott worked on
multiparameter eigenvalue problems, difference equations orthogonal
bipolynomials and (in collaboration) on elasticity and numerical
construction of special functions, There can be few members of the group
whose work has touched so many facets of our subject.

(I am indebted to Professor Robert Thomas for much of the information in
this notice.)

Topic #8  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Daniel Lozier <dlozier@nist.gov>
Subject: Postdoctoral Opportunity in Computation of Special Functions

This research opportunity focuses on improving the numerical support of
higher transcendental functions in parallel and other advanced
computational settings through development of algorithms, software and
test procedures.  An applicant with strong preparation in classical
mathematical analysis, especially complex analysis, is sought.  Other
relevant preparation includes experience in numerical analysis, theory of
special functions and computer science.

Emphasis in algorithm development is placed on methods for generating
numerical values of special functions for complex values of their
arguments and parameters.  For example, in conjunction with asymptotic and
other series expansions, differential and difference equations can be
solved in parallel to form stable and effective algorithms in the complex
domain.  Detailed mathematical analysis is required to bound, or estimate,
truncation errors and optimize algorithmic parameters.

Emphasis in software and test procedure development is placed on
construction of robust and highly reliable packages and systems. The
purpose is to fill gaps and correct defects that exist in currently
available library software for special functions, and to provide a
user-oriented test service capable of being tailored to very specific
needs.  Progress in algorithm development is fundamental to these
applications, as is the use of advanced Internet communications and
parallel computing techniques.

This Postdoctoral Research Associateship is administered by the National
Research Council, Washington, DC.  Only US citizens are eligible.  Its
tenure is two years starting not earlier than July 1, 1997, and not later
than February 1, 1998.  Applications must be mailed by January 15, 1997.
The doctorate must have been received less than five years before
application.  The base salary is $45,500.  For further information,
contact as soon as possible the Research Adviser for this Associateship:

  Dr. Daniel W. Lozier
  Building 820, Room 365
  Applied and Computational Mathematics Division
  National Institute of Standards and Technology
  Gaithersburg, MD 20899
  E-mail: dlozier@nist.gov, telephone: (301) 975-2706.

Topic #9  ---------------  OP-SF NET  ---------------- November 15, 1996
From: R. Alvarez-Nodarse <renato@dulcinea.uc3m.es>
Subject: Report of Madrid Workshop on Orthogonal Polynomials in Mathematical

A total of 74 participants engaged in friendly discussions and a pleasant
atmosphere accompanied the meeting. Thirteen Spanish institutions were
represented by 53 people and another thirteen foreign institution by the
rest. Each of the five invited speakers gave two one-hour lectures:

- Natig Atakishiev: (Instituto de Investigaciones en Matematicas Aplicadas
     y en Sistemas. Univ. Nacional Autonoma de Mexico. Cuernavaca.
     Mexico.) Difference Equations and Some of their Solutions.
     Ramanujan-type Continuous Measures for Classical q-Polynomials.

- Jesus S. Dehesa: (Departamento de Fisica Moderna. Univ. de Granada,
      Spain.) Information Theory, Quantum Entropy and Orthogonal

- Yuri F. Smirnov: (Instituto de Fisica, Univ. Nacional Autonoma de
      Mexico, Mexico). Orthogonal polynomials of a Discrete Variable and
      Quantum Algebras SU_q(2) and SU_q(1,1). Hidden sl(2) Algebra of the
      Finite Difference Equations.

- H. T. Koelink: (Univ. of Amsterdam, The Netherlands.) Addition Formulas
      for q-Special Functions. Hecke algebras and q-Krawtchouk

- Alexander Aptekarev: (Keldysh Institute, Russian Academy of Sciences,
      Moscow.) Toda-type Dynamics for the Coefficients of Recurrence

The sessions were completed by thirteen half-hour communications. These short
communications were delivered by:

- Andre Ronveaux: Orthogonal Polynomials: Connection and Linearization

- Roeloef Koekoek: Recent Developments in the Research of Differential
    Operators for Generalized (Sobolev) Orthogonal Polynomials.

- Aldo Tagliani: Entropy-convergence, Instability in Stieltjes and
    Hamburger Moment Problems.

- Ramon Orive: Rational Approximation to Certain Functions with Branch

- Wolfgang Gawronski: On the Zeros of Classical Orthogonal Polynomials
    with Large Complex Parameters

- Lucas Jodar: A Matrix Formula for the Generating Function of the Product
    of Hermite Matrix Polynomials.

- Pierpaolo Natalini: Some New Sets of Relativistic Orthogonal

- Franciszek Szafraniec: Orthogonal polynomials in building models of the
      quantum harmonic oscillator.

- Federico Finkel: Quasi Exactly Solvable Potentials on the Line and
    Orthogonal Polynomials.

- Franz Peherstorfer: Periodic and quasiperiodic Toda lattices.

- Jorge Sanchez-Ruiz: Position and momentum information entropies of the
     harmonic oscillator and logarithmic potential of Hermite polynomials.

- Jorge Arvesu: The classical Laguerre polynomials in a relativistic
     quantum-statistical model.

- Antonio Duran: On orthogonal matrix polynomials.

- Jose Carlos Petronilho: On Some Polynomial Modifications of Measures.

All speakers were kindly invited to submit written versions of their talks
for the proceedings of the meeting which will be published in the near
future. The Workshop was dedicated in honour of Prof. Andre Ronveaux on
the occasion of his retirement from the University and his fruitful
mathematical life.

The organizing Committee was: Manuel Alfaro (Univ. de Zaragoza), Renato
Alvarez-Nodarse (Secretary) (Univ. Carlos III), Antonio Garcia Garcia
(Univ. Carlos III), Guillermo Lopez Lagomasino (Univ. Carlos III) and
Francisco Marcellan (Chairman) (Univ. Carlos III)

Topic #10  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Richard Askey <askey@math.wisc.edu>
Subject: Bibliography on Orthogonal Polynomials

Information about the book:

A bibliography on orthogonal polynomials,
Bulletin of the National Research Council, Number 103
National Academy of Sciences, Washington D.C., 1940

During the depression of the 1930s, there were various projects funded by
different governments.  One of those in the United States was a
bibliography on orthogonal polynomials.  The nominal authors were listed
as Shohat, Hille and Walsh, and they did much of the background work,
preparing the outline format, and in Shohat's case knowing much of the
early Russian literature.  Much of the actual work was done by H.N. Laden
as you can read in two sentences which hint at this in the introduction.
The book is titled "A Bibliography on Orthogonal Polynomials", it was
published by the National Research Council of the National Academy of
Sciences, Washington, D.C., in 1940 as Number 103 of the Bulletin of the
National Research Council.

It is a 204 page book which starts with a list of 303 periodicals which
are referenced.  Then there is a seven page outline of information about
orthogonal polynomials.  This starts with special polynomials (Classical
OP) and includes three in two variables as well as the usual ones of
Jacobi, Laguerre and Hermite and special cases of them.  Each of these is
denoted by a letter which will be used later.  Then the area of general
orthogonal polynomials is broken down into many different types of
polynomials; finite interval of real axis, two finite intervals of real
axis, more than two, ... Jordan arc or closed curve in plane, etc., and
then a section on types of weight functions.  That is the first 1 1/3
pages.  The rest of the seven pages break up properties of OP into
different groups, listed by letters, Greek for such things as general
properties, expansions of functions, moment problem, application to
mathematical physics, etc.  Under each of these heading there are further
details.  For example, under Moment problem there is:  a. Criteria for the
character, determined or indeterminate, of the problem.  b. Solution,
which contains two subheadings:
   1. Infinitely many data,
   2. Finite many data.

Then the real information is given by an alphabetical list of
authors of papers first, and then books and theses.  Here is one

Adams, J.C.
  1. On the expression of the product of any two Legendre's coefficients
by means of a series of Legendre's coefficients.  [8]27(1878)63-71.

*[8] is Abstracts of the Papers Communicated to the Royal Society of
London: vol. 6.  The last refers to the last volume consulted.*

  P: alphab4-f, mu

* P means Legendre polynomials, alpha b 4 refers to general properties
for alpha, various representations for b and n-th derivative for 4.
The f is recurrence relation.  mu is evaluation of sums and definite
integrals involving OP (especially products of two or more OP).*

In this case the title of the paper tells what is there.  In most
cases this is not true, and the outline if it were more easily
searched could be useful.  The attempt to make it searchable in the
book is at the end, where there are 7 pages under the title Abbreviated
Topical Index.  The first is Hermite polynomials.  There are 34
lines of which the following is the first:

Adamoff 2; Agronomoff 1; Aitken 1; Aitken and Oppenheim 1; Angelesco 7,

and this is followed by 13,15,17; etc on the next line.  I have known
of this book for over 40 years and have owned a copy for more than 20.
I have successfully used it for finding something to use in research
once or twice, and for historical purposes a few more than that.

Topic #11  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Rene Swarttouw <rene@cs.vu.nl>
Subject: Extended version of Askey-Wilson-scheme report

Roelof Koekoek and Rene' Swarttouw are currently working on an extended
version of their report

     The Askey-scheme of hypergeometric orthogonal polynomials and its
     q-analogue, Report 94-05, Delft University of Technology, Faculty
     TWI, 1994

This new version will include Rodrigues' type formulae, forward and backward
shift-operators, leading coefficients and the monic recurrence relations for
all the orthogonal polynomials in the Askey-Wilson-scheme. They are also
working on an update of the list of references.

Concerning the latter subject they urge users of the report (or the electronic
version see http://www.can.nl/~demo/AWscheme/index.html) to go through
the current bibliography and to
see if they are missing some important
references. If so, please contact Rene' Swarttouw by e-mail or send him a
preprint of the missing article(s).

We thank everybody for their cooperation.

Address for Rene' Swarttouw:

Free University of Amsterdam
De Boelelaan 1081
1081 HV Amsterdam
The Netherlands
E-mail: rene@cs.vu.nl

Topic #12  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Marvin Rosenblum <mr1t@virginia.edu>
Subject: Review of "Table of Integrals, Series, and Products, CD-ROM
           Version 1.0"

(Editors' note:
This review appeared earlier in Newsletter OP & SF, October 1996)

Table of Integrals, Series, and Products, CD-ROM Version 1.0
Edited by Alan Jeffrey
Academic Press, San Diego, California, USA, 1996, ISBN 0-12-294756-8

The venerable Gradshteyn and Ryzhik "Table of Integrals, Series, and
Products" was originally planned by Ryzhik, who was later joined by
Gradshteyn.  The English translation was first published in 1965, and five
editions of the volume followed in the next thirty years. In each edition
there were corrections of errors and extensions of the material. Ryzhik
died in World War II and Gradshteyn died during preparation for the fourth
(1980) edition. The subsequent editions were and are edited by Alan

The fifth edition of the book has been put on CD, which can be viewed from
an IBM PC (or compatible) running Microsoft Windows 3.1, or 95, or NT, on
a Mac, or on certain UNIX X-windows machines. Of course, there are minimum
DRAM constraints, which only the foolhardy would ignore.  I ran the CD
using Windows 3.1.  One can scan the book much as one can read the text of
the printed fifth edition. But here one wants more, much more.

The major question is whether one can efficaciously search the CD so as to
find integrals and/or integrands involving expressions that are of
interest to the user. The manufacturer's guide asserts that the CD-ROM
offers desktop access to the 20000 formulas for the integrals, sums, etc.
The TeX source code for most formulae is obtained by clicking on a nearby
icon. To perform the search one need study the TeX code for the expression
that occupies your interest, activate the search panel, and fill in some
variant of the studied TeX code. Wildcards are allowed.

The sad story here is that the search engine used preempts and prohibits
use of the vital TeX characters
(  ,  )  , < ,  >  , =
It is very difficult to adapt the search program to do something other
than find quotations of names of special functions. The TeX used on the CD
is AMS-TeX, which is at this time not a usual dialect and thus provides a
minor nuisance. I believe that the problem of designing a search mechanism
to find TeX encoded mathematical expressions is interesting and
challenging.  I think it would be of interest to check with the experts
working with the Latex3 project to see if they have suggestions on how it
might be done.

Topic #13  ---------------  OP-SF NET  ---------------- November 15, 1996
From: K. Srinivasa Rao <rao@imsc.ernet.in>
Subject: book announcement on Quantum Theory of Angular Momentum

The following book may be of interest to some of you:

"Quantum Theory of Angular Momentum: Selected Topics"
by K. Srinivasa Rao and V. Rajeswari,
published by Springer-Verlag and Narosa Publishing House (1993).

The topics selected for study in this 315-page research monograph

- Connection between the angular momentum coupling (3-j) and
     recoupling (6-j and 9-j) coefficients and generalized
     hypergeometric functions of unit argument.

- Transformation theory of generalized hypergeometric functions
     and the relation of the different 3-j coefficient forms
     (due to Van der Waerden, Wigner, Racah, Majumdar, Raynal).

- Relation between the 3-j coefficient and the Hahn polynomial,
     the 6-j coefficient and the Racah polynomial and their consequences
     for recurrence relations.

- Polynomial (or non-trivial) zeros of angular momentum
     - closed form, formal  binomial expansions for the 3-j,
       6-j and 9-j coefficients.
     - Degree 1 zeros and multiplicative Diophantine equations.
     - Polynomial zeros of higher degrees.
     - Polynomial zeros and exceptional Lie algebras.
     - Numerical algorithms for the generation of polynomial zeros.

- q-3-j and q-6-j coefficients and their relation to sets
     of basic hypergeometric series.

- Numerical computation of angular momentum coefficient :
     - The 3-j coefficient, using the set of six  3F2(1)'s.
     - The 6-j coefficient, using two sets of three and four 4F3(1)'s.
     - The 9-j coefficient, using the triple sum series.
     - Parallel computation of the 9-j coefficient, using the
          hierarchic formulae.

Fortran programs for the computation of the 3-j, 6-j and
9-j coefficients are included for use by atomic, molecular
and nuclear Physicists / Chemists.

This research monograph builds on the standard text book material
contained in, for example:

A.R. Edmonds (1957),
Angular Momentum in Quantum Physics,
Princeton Univ. Press.

and it leads the reader to the recent developments in the  selected
topics. The contents of this book supplement the results in

L.C. Biedenharn and J.D. Louck,
"Angular Momentum in Quantum Physics" and
"Racah-Wigner Algebra in Quantum Physics",
Encyclopaedia of Mathematics and its Applications, Vols. 8 and 9.

and the compilation of all the known
formulae in this field contained in the book :

D.A. Varshalovich, A.N. Moskalev and V.K. Khersonskii,
Quantum Theory  of Angular Momentum,
World Scientific (1988)
(English edition of the  original Russian publication Nauka, Leningrad, 1975).

Topic #14  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Tom Koornwinder <thk@wins.uva.nl>
Subject: Announcement of edited book on Symmetries and Integrability of
         Difference Equations

Symmetries and Integrability of Difference Equations
Edited by: Decio Levi, Luc Vinet and Pavel Winternitz
CRM Proceedings & Lecture Notes Vol.9
American Mathematical Society, 1996
ISBN: 0-8218-0601-7

This book is devoted to symmetries and integrability of difference
equations and q-difference equations and the theory of special functions
that occur as solutions of such equations. Techniques that have been
traditionally applied to solve linear and nonlinear differential equations
are now being adapted and applied to discrete equations.

This volume is based on contributions during the workshop on Symmetries
and Integrability of Difference Equations held in Esterel, Quebec, in May

The book treats these specific topics:
- Lie group and quantum group symmetries of difference and q-difference
- integrable and nonintegrable discretizations of continuous integrable systems
- integrability of difference equations
- discrete Painleve property and singularity confinement
- integrable mappings
- applications in statistical mechanics and field theories
- Yang-Baxter equations
- q-special functions and discrete polynomials
- q-difference integrable systems


   * M. J. Ablowitz, B. M. Herbst, and C. Schober -- On the numerics of
     integrable discretizations
   * R. Askey -- A brief introduction to the world of q
   * N. M. Atakishiyev -- A Ramanujan-type measure for the Al-Salam and
     Ismail biorthogonal rational functions
   * H. M. Babujian and R. Flume -- Knizhnik-Zamolodchikov equations and the
     algebraic Bethe ansatz
   * H. W. Capel and F. W. Nijhoff -- Integrable quantum mappings
   * I. Cherdantsev and R. Yamilov -- Local master symmetries of
     differential-difference equations
   * P. A. Clarkson and A. P. Bassom -- Backlund transformations and
     hierarchies of exact solutions for the fourth Painleve equation and
     their application to discrete equations
   * J. F. van Diejen -- On the diagonalization of difference
     Calogero-Sutherland systems
   * A. Doliwa and P. M. Santini -- The integrable dynamics of a discrete
   * V. Dorodnitsyn -- Continuous symmetries of finite-difference evolution
     equations and grids
   * R. Floreanini and L. Vinet -- Basic Bessel functions and q-difference
   * D. V. Fursaev and V. G. Kadyshevsky -- Difference equations and gauge
   * H. Frahm, A. R. Its, and V. E. Korepin -- An operator-valued
     Riemann-Hilbert problem associated with the XXX model
   * F. A. Grunbaum and L. Haine -- Orthogonal polynomials satisfying
     differential equations: The role of the Darboux transformation
   * J. Harnad -- Quantum isomonodromic deformations and the
     Knizhnik-Zamolodchikov equations
   * N. Joshi and P. J. Vassiliou -- Lie symmetries and linearizations of
     analytic discrete dynamical systems
   * E. G. Kalnins and W. Miller, Jr. -- q-Algebra representations of the
     Euclidean, pseudo-Euclidean and oscillator algebras, and their tensor
   * V. B. Kuznetsov -- 3F2(1) hypergeometric function and quadratic
     R-matrix algebra
   * D. Levi and P. Winternitz -- Lie point symmetries of differential
     difference equations
   * R. M. Mir-Kasimov -- The factorization method for the
     differential-difference relativistic Schrodinger equation and
   * A. Mironov -- Quantum deformations of tau-functions, bilinear
     identities and representation theory
   * J. Negro -- The factorization method and hierarchies of q-oscillator
   * F. W. Nijhoff and G. D. Pang -- Discrete-time Calogero-Moser model and
     lattice KP equations
   * Y. Ohta, K. Kajiwara, and J. Satsuma -- Bilinear structure and exact
     solutions of the discrete Painleve I equation
   * V. Papageorgiou, B. Grammaticos, and A. Ramani -- Integrable difference
     equations and numerical analysis algorithms
   * M. Rahman -- An integral representation of the very-well-poised
     8psi8 series
   * M. Rahman and S. K. Suslov -- Singular analogue of the Fourier
     transformation for the Askey-Wilson polynomials
   * A. Ramani, B. Grammaticos, and V. Papageorgiou -- Singularity
   * A. Ronveaux, S. Belmehdi, E. Godoy, and A. Zarzo -- Recurrence relation
     approach for connection coefficients. Applications to classical
     discrete orthogonal polynomials
   * R. Sahadevan, G. B. Byrnes, and G. R. W. Quispel -- Linearisation of
     difference equations using factorisable Lie symmetries
   * A. B. Shabat -- First integrals of the infinite Toda lattice
   * E. Sorace -- Non semisimple quantum groups and "Exponential Mappings"
   * V. Spiridonov, L. Vinet, and A. Zhedanov -- Discrete Schrodinger
     equation, Darboux transformations, and orthogonal polynomials
   * L. A. Takhtajan -- Integrable cellular automata and AKNS hierarchy
   * C. M. Viallet -- On some rational Coxeter groups

Topic #15  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Hans J. Haubold <haubold@ekpvs2.dnet.tuwien.ac.at>
Subject: Mathai Festschrift

I would like to draw your attention to the International Journal of
Mathematical and Statistical Sciences, June 1995, Vol. 4, No.1, 1-130,
containing A Festschrift in Celebration of Professor A.M. Mathai's
Sixtieth Birthday.


- Foreword by S.B. Provost
- Publications of A.M. Mathai
- S.Cakmak, D.A.S.Fraser, P.McDunnogh, and N.Reid: Likelihood
     centered asymptotic model exponential and location model
- H.J.Haubold: An analytic solar model - Physical principles and
     mathematical structures.
- S.Kounias: Poisson approximation and Bonferroni bounds for the
     probability of the union events.
- I.B.MacNeill, Y.Mao, L.Xie, and S.M.Tang: Segmented models for
     age-period-cohort cancer data.
- A.M.Mathai and P.G.Moschopoulos: The distribution of the
     standard F-ratio in one-way ANOVA with multinomially
     distributed cell sizes.
- G.Pederzoli: Integral and series representations of a G-
     function through statistical techniques.
- S.B.Provost and E.M.Rudiuk: Moments and densities of test
     statistics for covariance structures.
- W.Y.Tan and M.L.Tiku: On a sampling distribution of the F-
     ratio in random effect models.
- D.S.Tracy and N.S.Mangat: Respondent's privacy hazards in
     Moors' randomized response model - A remedial strategy.

Topic #16  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Hans J. Haubold <haubold@ekpvs2.dnet.tuwien.ac.at>
Subject: Announcement of book on Zonal Polynomials

The following book was published recently and is being recommended to the
members of the activity group:

A.M.Mathai, S.B.Provost, and T.Hayakawa: Bilinear Forms and
Zonal Polynomials, Lecture Notes in Statistics Vol. 102,
Springer-Verlag,  Berlin and New York 1995, 376pp.

The book covers bilinear forms in real random vectors and their
generalizations as well as zonal polynomials and their applications with
respect to generalized quadratic and bilinear forms. The book begins with
the basic principles of the two fields and develops their mathematics and
statistics up to recent research results from the point of view of theory.
Detailed proofs may satisfy the mathematician while detailed examples may
inspire the physicist, particularly those working in the field of quantum
theory. Applications of the results are emphasized in extensive numbers of
exercises and references. The book is a rich source of material not yet
brought to the attention of physicists.

Topic #17  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Wolfram Koepf <koepf@zib.de>
Subject: Announcement of Edited book on Mathematical Analysis, Wavelets and
         Signal Processing

Mathematical Analysis, Wavelets and Signal Processing
Edited by Mourad E.H. Ismail, M. Zuhair Nashed, Ahmed I. Zayed,
and Ahmed F. Ghaleb
Contemporary Mathematics 190, AMS, January 1996, 354 pp.,
paperback, ISBN 0-8218-0384-0

Contributors include both mathematicians and engineers presenting their
ideas on new research trends. This book emphasizes the need for
interaction between mathematics and electrical engineering in order to
solve signal processing problems using traditional areas of mathematical
analysis such as sampling theory, approximation theory, and orthogonal

Topic #18  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Wolfram Koepf <koepf@zib.de>
Subject: Announcement of book on Polynomials and Polynomial Inequalities

Polynomials and Polynomial Inequalities
By P. Borwein and T. Erdelyi
Graduate Texts in Mathematics 161, Springer, Berlin,
1995, 480 pp., hardcover DM 98, ISBN 0-387-94509-1

Polynomials pervade mathematics, virtually every branch of mathematics
from algebraic number theory and algebraic geometry to applied analysis
and computer science, has a corpus of theory arising from polynomials. The
material explored in this book primarily concerns polynomials as they
arise in analysis, focusing on polynomials and rational functions of a
single variable. The book is self-contained and assumes at most a
senior-undergraduate familiarity with real and complex analysis. After an
introduction to the geometry of polynomials and a discussion of
refinements of the Fundamental Theorem of Algebra, the book turns to a
consideration of various special polynomials. Chebyshev and Descartes
systems are then introduced, and Muntz systems and rational systems are
examined in detail.  Subsequent chapters discuss denseness questions and
the inequalities satisfied by polynomials and rational functions.
Appendices on algorithms and computational concerns, on the interpolation
theorem, and on orthogonality and irrationality conclude the book.

Contents: Introduction and Basic Properties - Some Special Polynomials -
Chebyshev and Descartes Systems - Denseness Questions - Basic Inequalities
- Inequalities in Muntz Spaces - Inequalities in Rational Function Spaces

Appendices: Algorithms and Computational Concerns - Orthogonality and
Irrationality - An Interpolation Theorem - Inequalities for Generalized
Polynomials - Inequalities for Polynomials with Constraints.

Topic #19  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Richard Askey <askey@math.wisc.edu>
Subject: The Collected Works of Lars Onsager

"The Collected Works of Lars Onsager", editors P.C. Hemmer, H. Holden and
S. Kjelstrup Ratkje, World Scientific, Singapore, New Jersey, London
and Hong Kong, 1996.

Onsager's unpublished Ph.D. thesis is printed here.  The title is
"Solutions of the Mathieu equation of period 4 pi and certain related

The biographical memoir on Onsager by C. Longuet-Higgins and M. Fisher is
fascinating.  Before he started, at 17, to study chemical engineering
at Norges Tekniske Hoiskole in Trondheim, Onsager had bought a copy of
Whittaker and Watson's "Modern Analysis" and worked through most of the
problems.  It remained a favorite of his, and the elliptic functions he
learn there were used in his solution of the two dimensional Ising model.

Further information on Onsager and many very interesting stories were also
given in J. Statistical Physics, vol 78 (1995), no. 1-2.

Topic #20  ---------------  OP-SF NET  ---------------- November 15, 1996
From: OP-SF Net editor <thk@wins.uva.nl>
Subject: ftp site for papers in Orthogonal Polynomials and Special Functions

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.  One can approach the archive by anonymous ftp to
unvie6.un.or.at, directory siam, or at the WWW address
ftp://unvie6.un.or.at/siam .  See the file 00contents.ftpsite in the
submissions directory for the contents (titles, authors, filenames) of the
directories opsf and abstracts.  This list of contents is in chronological
order of submission.  The most recent contributions will just reside as
files in the submissions directory, and are not yet documented in the list
of contents.

Hans Haubold is sending regular information about new submissions to a
large mailing list. Please contact him <haubold@Relay1.Austria.EU.net> if
you want to be added to this mailing list or if your email address on the
list is no longer correct.

Since July 15, the following papers have been submitted to the archive:

H.J. Haubold and A.M. Mathai, On thermonuclear reaction rates.
(see siam/opsf/haubold-mathai6.tex)

J.F. van Diejen, Confluent hypergeometric orthogonal polynomials
related to the rational quantum Calogero system with harmonic
(see siam/opsf/diejen3.tex)

N.M. Temme, Asymptotics and numerics of polynomials that are
related to Daubechies wavelets.
(see siam/opsf/temme-daub.ps)

K. Stempak and W. Trebels, Hankel multipliers and transplantation
(see siam/opsf/stempak-trebels.tex)

V.B. Kuznetsov and E.K. Sklyanin, Separation of variables and integral
relations for special functions.
(see siam/submissions/kuznetsov-sklyanin.tex

Topic #21  ---------------  OP-SF NET  ---------------- November 15, 1996
From: The Editors <thk@wins.uva.nl>, <muldoon@yorku.ca>
Subject: Changes of Address, WWW pages. etc.

Jeff Geronimo (permanently at Georgia Inst. of Technology, Atlanta, GA,
USA)  will stay in France at least until the end of June 1997. He is part
time at Saclay, part time at Paris VI with Albert Cohen. He can be reached

Jeff Geronimo
CEA Saclay
91190-Gif-sur-Yvette Cedex
email: jeff@wasa.saclay.cea.fr

Throughout the email addresses, URL's and ftp address of Erik Koelink,
Tom Koornwinder and Jasper Stokman (Univ. of Amsterdam) please replace
fwi by wins:

Erik Koelink, email: koelink@wins.uva.nl
WWW: http://turing.wins.uva.nl/~koelink/

Tom Koornwinder, email: thk@wins.uva.nl
WWW: http://turing.wins.uva.nl/~thk/

Jasper Stokman, email: jasper@wins.uva.nl
WWW: http://turing.wins.uva.nl/~jasper/

ftp site for Koelink, Koornwinder, Stokman:
ftp.wins.uva.nl, in directory pub/mathematics/reports/Analysis

The old addresses will remain valid for a while.

Bruce Berndt has a home page:

The Ramanujan Journal has a home page containing the contents of
Vol. 1, No. 1, January 1997, an editorial and further information:


The contents of J. Math. Analysis and Applications and of
J. Symbolic Computation can be found via the Academic Press site


The electronic preprint archive solv-int occasionally contains papers
which are relevant for the field of OP & SF. See WWW:


Topic #22  ---------------  OP-SF NET  ---------------- November 15, 1996
From: OP-SF Net editor <thk@wins.uva.nl>
Subject: Part 33 of 1991 Mathematics Subject Classification

Classification:    33-XX Special functions, {33-XX deals with the
                   properties of functions as functions.  For orthogonal
                   functions, See also 42Cxx; for aspects of
                   combinatorics, See 05Axx; for number-theoretic aspects,
                   See 11-XX; for representation theory, See 22Exx}

     33-00   General reference works (handbooks, dictionaries,
               bibliographies, etc.)
     33-01   Instructional exposition (textbooks, tutorial papers, etc.)
     33-02   Research exposition (monographs, survey articles)
     33-03   Historical (must be assigned at least one classification
               number from Section 01)
     33-04   Explicit machine computation and programs (not the theory
               of computation or programming)
     33-06   Proceedings, conferences, collections, etc.
   33Bxx     Elementary classical functions
     33B10   Exponential and trigonometric functions
     33B15   Gamma, beta and polygamma functions
     33B20   Incomplete beta and gamma functions (error functions,
               probability integral, Fresnel integrals)
     33B99   None of the above but in this section
   33Cxx     Hypergeometric functions
     33C05   Classical hypergeometric functions, $_2F_1$
     33C10   Bessel and Airy functions, cylinder functions, $_0F_1$
     33C15   Confluent hypergeometric functions, Whittaker functions,
     33C20   Generalized hypergeometric series, $_pF_q$
     33C45   Orthogonal polynomials and functions (Chebyshev, Legendre,
               Gegenbauer, Jacobi, Laguerre, Hermite, Hahn, etc.)
     33C50   Orthogonal polynomials and functions in several variables
     33C55   Spherical functions, spherical harmonics, ultraspherical
     33C60   Hypergeometric integrals and functions defined by them
               ($E$, $G$ and ${H}$ functions)
     33C65   Appell, Horn and Lauricella functions
     33C70   Other hypergeometric functions and integrals in several
     33C75   Elliptic integrals as hypergeometric functions
     33C80   Connections with groups, algebras, root systems and related
     33C90   Applications
     33C99   None of the above but in this section
   33Dxx     Basic hypergeometric functions
     33D05   $q$-gamma functions, $q$-beta functions and integrals
     33D10   Basic theta functions
     33D15   Basic hypergeometric functions in one variable
     33D20   Generalized basic hypergeometric series
     33D45   Basic orthogonal polynomials and functions in one and
               several variables
     33D55   Basic spherical functions, spherical harmonics (continuous
               and discrete)
     33D60   Basic hypergeometric integrals and functions defined by
     33D65   Bibasic functions and multiple bases
     33D70   Other basic hypergeometric functions and integrals in
               several variables
     33D80   Connections with groups, algebras, and related topics
     33D90   Applications
     33D99   None of the above but in this section
   33Exx     Other special functions
     33E05   Elliptic functions and integrals
     33E10   Lame, Mathieu, and spheroidal wave functions
     33E15   Other wave functions
     33E20   Other functions defined by series and integrals
     33E30   Other functions coming from differential, difference and
               integral equations
     33E99   None of the above but in this section

Topic #23  ---------------  OP-SF NET  ---------------- November 15, 1996
From: Jan Felipe van Diejen
Subject: Montreal Workshop on Calogero-Moser-Sutherland systems

(late submission to this issue)

During the period March 10-15, 1997, the CRM organizes a

Keynote Speakers:
F.     Calogero      (Universit\`a di Roma)
J.K.   Moser*        (E.T.H.)
B.     Sutherland    (University of Utah)

Invited Speakers:
B.L.   Altshuler     (NEC Research Institute)
T.     Baker         (Melbourne University)
D.     Bernard       (Saclay)
R.K.   Bhaduri       (McMaster University)
H.W.   Braden        (University of Edinburgh)
P.     Di Francesco  (University of North Carolina at Chapel Hill)
T.     Eguchi        (University of Tokyo)
B.     Enriquez      (Ecole Polytechnique de Palaiseau)
F.D.M. Haldane       (Princeton)
V.I.   Inozemtsev    (Joint Institute for Nuclear Research)
I.     Krichever*    (Columbia University)
P.     Mathieu       (Universit\'e Laval)
N.     Nekrasov      (Harvard)
M.A.   Olshanetsky   (Inst. of Theoretical and Exp. Physics)
V.     Pasquier      (Princeton)
A.P.   Polychronakos (University of Ioannina)
V.     Rubtsov*      (Inst. of Theoretical & Exp. Physics)
S.N.M. Ruijsenaars   (CWI)
H.     Saleur        (University of Southern California)
D.     Senechal*     (Universit\'e de Sherbrooke)
T.     Shiota        (Kyoto University)
E.K.   Sklyanin      (University of Tokyo)
A.     Varchenko     (University of North Carolina at Chapel Hill)
A.     Veselov       (Loughborough University)
M.     Wadati        (University of Tokyo)
G.     Wilson        (Imperial College)

* to be confirmed

Jan Felipe van Diejen & Luc Vinet

Information and Registration:

Louis Pelletier
Centre de Recherches Math\'ematiques
Universit\'e de Montr\'eal
C.P. 6128, succ. Centre-ville
Montr\'eal (Qu\'ebec) H3C 3J7

or electronically:
E-mail: ACTIVITES@CRM.UMontreal.CA
WWW   : http://www.CRM.UMontreal.CA

Topic #24  ---------------  OP-SF NET  ---------------- November 15, 1996
From: OP-SF Net editor <thk@wins.uva.nl>
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:

or   WWW:

Contributions to the OP-SF Net 4.1 should reach the email
address  poly@siam.org  before January 1, 1997.

The Activity Group also sponsors a Newsletter edited by Wolfram Koepf.
Deadline for submissions to be included in  February 1997 issue
is January 15, 1997.

Please send your Newsletter contributions directly to the Editor:

Wolfram Koepf
Takustr. 7
D-14195 Berlin, Germany
tel.: +49-30-841 85-348
fax:  +49-30-841 85-269
email: koepf@zib.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. 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   -
-  special functions and orthogonal polynomials community.  This      -
-  includes announcements of conferences, forthcoming books, new      -
-  software, electronic archives, research questions, job openings.   -
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-            pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir -
-  WWW home page of this Activity Group:                              -
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-              Charles Dunkl, Chair                                   -
-              Tom H. Koornwinder, Vice Chair and OP-SF Net editor    -
-              Nico M. Temme, Secretary                               -
-              Willard Miller, Jr., Program Director                  -
-      The appointed officers are:                                    -
-              Wolfram Koepf, Newsletter editor                       -
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