Volume 4, Number 2

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-                                                                     -
-                                           March 15, 1997            -
-      O P - S F   N E T                    Volume 4, Number 2        -
-      ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~        -
-      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. Minisymposium on "Handbooks for Special Functions and the
           World Wide Web"
    2. University of Wisconsin Centenary Conference, including
           minisymposium on special functions
    3. VIII International Conference on Symmetry Methods in Physics,
           Dubna, Russia
    4. Symposium on orthogonal polynomials in Sevilla
    5. Report from Madras Workshop on Special Functions & Differential
    6. Bourbaki Lecture on Dunkl operators
    7. Death of Louis Auslander
    8. Reprinting of Olver's "Asymptotics and Special Functions"
    9. Proceedings of 1995 Toronto Workshop on "Special Functions,
           q-Series and Related Topics"
   10. The Ramanujan Journal
   11. End of Problem Section in SIAM Review?
   12. Compiled Booklist and list of Electronic Services (Wolfram Koepf)
   13. ftp site for papers in Orthogonal Polynomials and Special
   14. Changes of Address, WWW Pages, etc.
   15. Obtaining back issues of OP-SF Net and submitting contributions
           to OP-SF Net and Newsletter

Calendar of events:                                      see issue/topic:

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 and 4.2 #2
June 3-7: First ISAAC Conference (International Society for Analysis,
        its Applications and Computation) in Newark, Delaware       4.1 #2
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
         including Minisymposium on "Handbooks for Special Functions
         and the World Wide Web"                                    4.2 #1
July 14-18: 9th International Conference on Formal Power Series
         and Algebraic Combinatorics, Vienna, Austria               3.4 #7
July 28 - August 2: VIII International Conference on Symmetry
          Methods in Physics, Dubna, Russia                         4.2 #3
September 22-26: VIII Simposium sobre Polinomios Ortogonales y
          Aplicaciones, Seville, Spain                   3.5 #5 and 4.2 #4

Topic #1  --------------   OP-SF NET 4.2  ------------- March 15,1997
From: Willard Miller, Jr. <miller@ima.umn.edu>
Subject: Minisymposium on "Handbooks for Special Functions and the
                             World Wide Web"

The minisymposium will be held at the July 14-18 1997 SIAM Annual Meeting
in Stanford as an initiative of the SIAM Activity Group on Orthogonal
Polynomials and Special Functions.  Dick Askey and Willard Miller are
co-organizers. The principal handbooks on special functions, the "Bateman
Project" and the NIST "Handbook of Mathematical Functions"  are among the
most useful, widely consulted technical volumes ever published, but they
are now out of date, due to rapid research progress and to revolutionary
changes in technology. The Minisymposium will feature talks by
representatives of the groups that are proposing to update the Bateman
Project and Abramowitz & Stegun, respectively, and talks with critiques of
those CD-Rom and WWW handbook projects that are already available. The
Minisymposium will conclude with a general discussion concerning the
appropriate format and structure for handbook projects, and funding
possibilities.  Confirmed talks to date are the following:

Daniel W. Lozier
Mathematical and Computational Sciences Division
National Institute of Standards and Technology
Gaithersburg, MD 20899

Title: Toward a Revised NBS Handbook of Mathematical Functions

Abstract:  A modernized and updated revision of Abramowitz and Stegun,
Handbook of Mathematical Functions, first published in 1964 by the
National Bureau of Standards, is being planned for publication on the
World Wide Web.  The authoritative status of the original will be
preserved by enlisting the aid of qualified mathematicians and scientists.
The practical emphasis on formulas, graphs, and numerical evaluation will
be extended by providing an interactive capability to permit generation of
tables and graphs on demand.

Mourad E. H. Ismail
Department of Mathematics
University of  South Florida
Tampa, Florida, 33620

Title: The Askey-Bateman Project

Abstract: We hope to update the Bateman Project to reflect the
developments in the subject over the last fifty years and cover topics
of importance that were not covered in the initial project. A
presentation will be made as to the current state of this project, the
need for it, and a sketch of the contents and the personnel to be
involved. Suggestions, recommendations, criticisms and any useful
input will be welcome and greatly appreciated.

Richard Askey
Department of Mathematics
University of Wisconsin
480 Lincoln Drive
Madison, WI 53706

Title: Handbooks of special functions through the decades

Abstract:  Handbooks of special functions have been some of the
most widely used mathematics books.  Features of some of the better
ones will be described and some uses will be illustrated.

Further information on the SIAM meeting may be found at the URL:
or by email from meetings@siam.org

Topic #2  --------------   OP-SF NET 4.2  ------------- March 15,1997
From: Charles Dunkl <cfd5z@virginia.edu>
Subject: University of Wisconsin Centenary Conference, including
        minisymposium on special functions

Here is the most up-to-date list of speakers and titles for the
minisymposium on special functions to be held during the University of
Wisconsin Centenary Conference to be held in Madison, Wisconsin, May
22-24, 1997. (See OP-SF NET 3.4 #5).  I do not have a time schedule, but
there will be two sessions as indicated. The speakers have all accepted.

Session 1
Gilbert G. Walter, University of Wisconsin-Milwaukee,
   "Wavelets and special functions"

Steve Milne,  Ohio State University,
   "Sums of squares, Jacobi elliptic functions and continued
    fractions, and Schur functions"

Paul Nevai, Ohio State University,
   "Orthogonal polynomials on an arc of the unit circle"

Alan Schwartz, University of Missouri-St. Louis ,
   "Multivariate orthogonal polynomials, measure algebras,
    and differential operators"

Charles F. Dunkl, University of Virginia,
  "Generalized Hermite polynomials and root systems"

Session 2
George Gasper,  Northwestern University,
  "q-Analogues of Erdelyi's fractional integrals and applications"

Paul Terwilliger,  University of Wisconsin-Madison,
  "Leonard Systems and the q-Racah polynomials"

Anatol N. Kirillov, CRM , Universite de Montreal,
  "Quantum Schur functions and quantum Schubert polynomials"

Mourad Ismail,  University of South Florida,
  "Toda lattice and orthogonal polynomials"

Dennis Stanton,  University of Minnesota,
   "Applications of cubic hypergeometric  transformations"

Topic #3   --------------  OP-SF NET 4.2 --------------- March 15, 1997
From: G. Pogosyan <symphys8@thsun1.jinr.dubna.su>
Subject: VIII International Conference on Symmetry Methods in Physics,
                   Dubna, Russia

The VIII International Conference on Symmetry Methods in Physics will be
held in Dubna, Russia during July 28 - August 2, 1997.  This Conference,
organized by the Bogoliubov Laboratory of Theoretical Physics of the Joint
Institute for Nuclear Research, is dedicated to the 80th anniversary of
Professor Smorodinsky's birth.

One of the topics of the conference will be
"Quantum groups and q-special functions".
See the web page mentioned below for further topics.

Plenary speakers are ( * means to be confirmed):

M.Charlton (London)
V.K.Dobrev (Sofia)
H.D.Doebner * (Clausthal)
J.P.Draayer (Baton Rouge)
F.Iachello (New Haven)
A.U.Klimyk * (Kiev)
P.Kulish (St.Petersburg)
V.B.Kuznetsov (Leeds)
F.J.Lambert * (Brussels)
I.Meshkov (Dubna)
W.Miller Jr. (Minneapolis)
P.Van Moerbeke (Louvain-la-Neuve)
A.Yu.Morozov (Moscow)
A.M.Perelomov (Zaragoza)
L.O'Raifeartaigh (Dublin)
N.Reshetikhin * (Berkeley)
A.B.Shabat (Moscow)
D.V.Shirkov (Dubna)
G.Sudarshan * (Austin)

It is possible to apply for giving a contributed talk.
The Proceedings of the conference will be published.

Persons interested in participating are kindly asked
to apply before March 31, 1997 by fax or e-mail.

For further information and for the application form see the Web page


or send an email to the chairman of the local organizing committee
Dr. George Pogosyan <symphys8@thsun1.jinr.dubna.su>.

Topic #4   --------------  OP-SF NET 4.2 --------------- March 15, 1997
From: OP-SF Net editor <thk@wins.uva.nl>
Subject: Symposium on orthogonal polynomials in Sevilla

The VIII Simposium sobre Polinomios Ortogonales y Aplicaciones
in Sevilla, Spain during September 22-26, 1997 was announced in
OP-SF Net 3.5, Topic #5. Updated information can be found on the web page


For the reader's convenience we give here a list of plenary speakers:

   * D. Alpay: Orthogonal matrix polynomials and reproducing kernel spaces
   * Alexander I. Aptekarev (no title yet)
   * Richard Askey: Combinatorics and the classical orthogonal polynomials
   * Christian Berg: Indeterminate moment problems
   * Doron Lubinsky: Orthogonal polynomials for exponential weights
   * Andrei Martinez: On asymptotic properties of Sobolev orthogonal
   * Paul Nevai: The L^p (p>2) variant of Steklov's conjecture fails too
   * Evgeni Rakhmanov: On asymptotics of orthogonal polynomials of a
     discrete variable
   * Edward B. Saff (no title yet)
   * Herbert Stahl: Spurious poles of Pade approximants
   * Vilmos Totik: General orthogonal polynomials

Registration should be done not later than May 30, 1997.
Send email to  8spoa@obelix.cica.es

Topic #5  --------------   OP-SF NET 4.2  ------------- March 15,1997
From: Tom Koornwinder <thk@wins.uva.nl>, Walter Van Assche

Subject: Report from Madras Workshop on Special Functions & Differential
         Equations: Chennai (Madras), India, January 13-24, 1997

A workshop on special functions and differential equations was held at the
"Institute of Mathematical Sciences" in Chennai (formerly known as Madras)
in India, from January 13 to January 24, 1997.  The main organizer was K.
Srinivasa Rao, who succeeded in getting about 75 participants, with
approximately two thirds of them from India. The other participants were
from Belgium (7), The Netherlands (3), Australia (2), New Zealand,
Finland, Canada, Poland, Germany, Austria, France, and Italy (each 1), and
some people from India working temporarily abroad.

The background of speakers and participants was partly from pure and
applied mathematics and partly from mathematical and theoretical physics.
At least half of the lectures dealt with the first conference theme,
special functions. The other theme of differential equations was
approached both from the analytic side and from the numerical side.  A few
lectures merged both themes. All lectures were plenary and invited and had
a standard length of 45 minutes. There were quite a few minicourses
consisting of two or three lectures.  The topics of these minicourses
ranged over:  Ramanujan's mock theta functions;  connection and
linearization coefficients for orthogonal polynomials;  generalizations of
Laguerre polynomials by adding (a derivative of)  delta(x)  to the weight
function;  applications of 3j, 6j and 9j coefficients to special function
theory;  irrationality and transcendence proofs of some famous numbers by
approximation theory;  special functions associated with root systems;
creation operators for Jack and Macdonald polynomials;  numerical methods
for solving o.d.e.'s;  parallel algorithms for solving o.d.e.'s;
non-linear quantum mechanics;  the uncertainty principle;  nonlinear
evolution equations.  D.-N. Verma (of Verma module fame) gave some
informal seminars on Lie theory, Clebsch-Gordan coefficients and related
matters, and Tom Koornwinder filled a gap in the program by giving a
seminar lecture on Zeilberger's algorithm.

The workshop even made the local newspaper and television due to a special
lecture "A nuclear-weapon free world: desirable? possible? probable?" by
F. Calogero, secretary general of the Pugwash conferences on science and
world affairs, which was attended by his excellency R. Venkataraman,
former president of India.

During the opening ceremony of the workshop, R.P. Agarwal gave a survey on
special functions in India during the last century. Among others, the
theory of q-special functions, the (Miller type) Lie theoretic approach to
special functions, and applications to theoretical physics and probability
theory are well represented nowadays in India. Professor Agarwal concluded
his survey with a call to avoid superficial work and to look always for
deep results.  Tom Koornwinder, as vice-chair of our SIAM Activity Group,
was asked to make some remarks in reply.  He indicated some further active
research areas in our field, such as special functions of several
variables, their relation with certain algebraic structures (Lie groups
and algebras, root systems, quantum groups, Hecke algebras), the general
theory of orthogonal polynomials (including the Sobolev inner products),
computer algebra methods for finding hypergeometric identities, and the
application of special functions in real life situations (engineering).
Some of these aspects indeed were the subject of subsequent lectures.

During the workshop there was an informal meeting for founding a Society
for Special Functions & Applications in India. Its aim will be to promote
research in this area, to inform people of what is going on, and possibly
to create a new India-based forum for bringing out research publications
of international standard on special functions. Application forms for
life-long membership are already available.  Interaction with our SIAM
activity group looked desirable to all present at the discussions,
certainly concerning the Newsletter.

A very extensive cultural program was prepared by the organizers. Among
the events were a dance performance, a concert of traditional Indian
music, a trip to a drive-in movie to see a Tamil version of Mrs.
Doubtfire, and on Sunday a visit to the temple cities Kancheepuram and
Mahabalipuram to visit the temples (barefoot of course) and to do business
with the local sandal makers and sculptors (bargaining skill is

Ramanujan is of course very closely connected with Chennai and a visit to
the Ramanujan museum and the Ramanujan Institute for Mathematical Sciences
of the University of Madras was therefore a natural part of the program.
The Ramanujan museum is a rather recent realisation located in a
mathematics education center. Srinivasa Rao gave a lecture on the life and
work of Ramanujan and afterwards we were able to see the displays in the
museum. Some of Ramanujan's work is very suitable for use in mathematics
courses at all levels and the Ramanujan museum wants to advertize this
idea.  Our visit to the museum ended with a delicious high tea organized
with great care and effort by the mathematics education center.

All western participants were impressed by the quality of the hosting
Institute of Mathematical Sciences, the great hospitality, and (for
newcomers) the fascinating intricacies of Indian culture and society. The
efforts of prof. K. Srinivasa Rao to make this workshop into a success are
really beyond praise.

Tom H Koornwinder
Walter Van Assche

Topic #6   --------------  OP-SF NET 4.2 --------------- March 15, 1997
From: OP-SF Net editor <thk@wins.uva.nl>
Subject: Bourbaki Lecture on Dunkl operators

On March 1, 1997 Gert Heckman (Catholic University of Nijmegen)
delivered a lecture in the Seminaire Bourbaki, Paris on "Dunkl operators".
We congratulate Gert Heckman and Charles Dunkl.

Topic #7  --------------   OP-SF NET 4.2  ------------- March 15,1997
From: Dick Askey <askey@math.wisc.edu>
Subject: Death of Louis Auslander

     Louis Auslander died at 68 on February 25, 1997.  His early work was
on differential geometry.  Later he worked on nilpotent Lie groups, and
this led to the study of theta functions.  Two of his books are "Abelian
Harmonic Analysis, Theta Functions and Function Algebras on a
Nilmanifold", Springer, 1975, and "Lecture Notes on Nil-Theta Functions",
CBMS lectures published by American Mathematical Society, 1977.  His later
work was on finite Fourier transforms, which also involves some special
functions.  His expository paper with Tolimieri: "Is computing the finite
Fourier transform pure or applied mathematics?", BAMS (New Series), 1
(1979)  847-897, has been cited frequently, and is worth reading.  The
first of the books mentioned above is also joint with Richard Tolimieri.
     Auslander attended the Oberwolfach meeting on special functions and
group theory run by Askey, Koornwinder and Schempp in 1983.  He was
fascinated by some of the work described there, as were some of us by
his work.

Topic #8  --------------   OP-SF NET 4.2  ------------- March 15,1997
From: Frank Olver <olver@ipst.umd.edu>
Subject: Reprinting of "Asymptotics and Special Functions"

Readers may be interested to learn that my book "Asymptotics and Special
Functions", originally published by Academic Press in 1974, has just been
reprinted by A.K. Peters, Ltd. It is again in hardback form and it lists
at $69. Copies can be ordered through booksellers (ISBN: 1-56881-069-5) or
directly from the publisher at 289 Linden Street, Wellesley, MA 02181;
email: akpeters@tiac.net.

Topic #9  --------------   OP-SF NET 4.2  ------------- March 15,1997
From: Martin Muldoon <muldoon@yorku.ca>
Subject: Workshop Proceedings on "Special Functions, q-Series and
                  Related Topics"

The proceedings volume for the 1995 Toronto Workshop on "Special
Functions, q-Series and Related Topics" (OP-SF NET 2.4, Topic #8) has now
appeared.  The following information is taken from the AMS Web Page.

"Special Functions, q-Series and Related Topics"
Edited by: Mourad E. H. Ismail (University of South Florida), David
R. Masson  (University of Toronto) and Mizan Rahman (Carleton University).

This book contains contributions from the proceedings at The Fields
Institute workshop on Special Functions, q-Series and Related Topics
that was held in June 1995. The articles cover areas from quantum groups
and their representations, multivariate special functions, q-series, and
symbolic algebra techniques as well as the traditional areas of
single-variable special functions. The book contains both pure and applied
topics and reflects recent trends of research in the various areas of
special functions.


     K. Alladi -- Refinements of Rogers-Ramanujan type identities
     B. C. Berndt, H. H. Chan, and L.-C. Zhang -- Ramanujan's class
             invariants with applications to the values of q-continued
             fractions and theta functions
     G. Gasper -- Elementary derivations of summation and transformation
             formulas for q-series
     R. W. Gosper, Jr. -- \int ^{m/6}_{n/4}\ln \Gamma (z)dz
     F. A. Grunbaum and L. Haine -- On a q-analogue of Gauss equation
             and some q-Riccati equations
     R. A. Gustafson and C. Krattenthaler -- Determinant evaluations and
             U(n) extensions of Heine's _2\phi _1-transformations
     M. E. H. Ismail, D. R. Masson, and S. K. Suslov -- Some generating
            functions for q-polynomials
     E. Koelink -- Addition formulas for q-special functions
     T. H. Koornwinder -- Special functions and q-commuting variables
     M. Noumi, M. S. Dijkhuizen, and T. Sugitani -- Multivariable
           Askey-Wilson polynomials and quantum complex Grassmannians
     P. Paule and A. Riese -- A Mathematica q-analogue of Zeilberger's
           algorithm based on an algebraically motivated approach to
           q-hypergeometric telescoping
     W. Van Assche -- Orthogonal polynomials in the complex plane and on
           the real line
     Y. Xu -- On orthogonal polynomials in several variables

     Appendix I: Program list of speakers and topics
     Appendix II: List of participants


     Publisher: American Mathematical Society
     Distributor: American Mathematical Society
     Series: Fields Institute Communications, ISSN: 1069-5265
     Volume: 14
     Publication Year: 1997
     ISBN: 0-8218-0524-X
     Paging: 277 pp.
     Binding: hardcover
     List Price: $82
     Institutional Member Price: $66
     Individual Member Price: $49
     Itemcode: FIC/14

Topic #10 --------------   OP-SF NET 4.2  ------------- March 15,1997
From: Frank G. Garvan <frank@math.ufl.edu>
Subject: The Ramanujan Journal

The Ramanujan Journal, an international journal devoted to the areas of
mathematics influenced by Ramanujan was announced in OP-SF NET 2-4, #15
Here is the Table of Contents of Volume 1, Number 1, January 1997:

                                                 Krishnaswami Alladi    5
   The Well-Poised Thread: An Organized Chronicle of Some Amazing
   Summations and Their Implications (Survey Article)
                                                    George E. Andrews   7
   Divisibility of Certain Partition Functions by Powers of Primes
                                            Basil Gordon and Ken Ono   25
   Ramanujan's Master Theorem for Hermitian Symmetric Spaces
                                                       Hongming Ding   35
   Ramanujan's Singular Moduli
              Bruce C. Berndt, Heng Huat Chan, and Liang-Cheng Zhang   53
   On the Ramanujan-Gollnitz-Gordon Continued Fraction
                                   Heng Huat Chan and Sen-Shan Huang   75
   Rogers-Ramanujan type Identities for Partitions with Attached Odd
                              George E. Andrews and J. Plinio Santos   91
   Lecture Hall Partitions
                          Mireille Bousquet-Melou and Kimmo Eriksson  101

The Home Page of The Ramanujan Journal is at the URL:

Topic #11 --------------   OP-SF NET 4.2  ------------- March 15,1997
From: OP-SF Net Editor <muldoon@yorku.ca>
Subject: End of Problem Section in SIAM Review?

We heard from Joop Boersma (Technical University Eindhoven) of a report
that SIAM Review is considering dropping its Problem Section. Boersma
would regret this very much. According to him the Problem Section provides
a forum where problems from Applied Analysis, in particular, can be
brought to the attention of a wider audience. He asks whether our Activity
Group can intervene.

Please send us your opinion. There has been some discussion among the
editors and other officers of the Activity Group.  Here are some extracts
from their comments:

Tom Koornwinder:
"The number of people submitting or solving any problems is only a small
minority. Part of these people invest a lot of time in these activities,
and try to deal with problem sections in many different journals.  Some
even form teams for this purpose (e.g., the well-known O.P. Lossers team
in Eindhoven). I think that it is not so harmful for this category of
people when a problem section in one journal will stop, because there are
many other journals (including our Newsletter)  where such sections will
remain.  More serious is Boersma's argument that researchers can call the
help of other specialists in such a way (for instance applied
mathematicians calling the help of specialists in special functions).
However I think that it is better not to hide such questions in a problem
section, but rather call it a section on research questions.  One other
point about this Problem section is that it also gave some more publicity
about Special Functions to the SIAM community (almost every issue of the
Problems section had at least one problem on SF).  In a sense that was
good, because OP & SF does not get much other coverage in SIAM News and
SIAM Review. On the other hand, by the very nature of a Problem Section,
the aspects of Special Functions being treated there emphasize the
"special" and the formula aspect of Special Functions, much less the
qualitative and conceptual sides of the field.  In this way such a Problem
Section can also help to maintain or strengthen existing prejudices
against special functions."

Martin Muldoon:
"The problems [in SIAM Review] are much too difficult. I suspect that many
other readers would agree and that may explain why the Section may be
chopped.  I believe that its main strength, compared to problem sections
in other journals, is that many of the problems arise from applications.
While it is true that it provides a way for applied mathematicians to call
on experts, in practice it is surely much too slow for this.  A member
once told me that he thought our Newsletter should not have a Problem
Section since it competes with and takes problems away from SIAM Review.
I answered that I thought that were more than enough good problems to go

Nico Temme:
"My opinion about problem sections in journals is that the reader should
have a fair chance, and that much detailed and technical expertise should
not be needed to solve the problems. In this sense it is good to have
a few places where one can find problems.  Nieuw Archief voor Wiskunde
offers only problems of which the solutions are known. But they had
difficult years some time ago to get good editors.

"In some cases the problems are too difficult for a non-introduced reader.
This is acceptable when the solution is not known.

"Usually I am not motivated to solve the first category. It is more
"educational" and it consumes too much time. When I see a problem with
a * in SIAM Review (which means an "open problem") I become interested.

"I think that there should be a place for both categories, and that it
should be clear where to find  both categories. SIAM Review has a long
tradition on this, and the journal is available in many places. ...

"I think that having a Problem Section in our Newsletter for open problems
is important and of interest to many readers."

Topic #12 --------------   OP-SF NET 4.2  ------------- March 15,1997
From: Wolfram Koepf <koepf@zib.de>
Subject: Compiled Booklist and Electronic Services

(This item appeared in The Activity Group's Newsletter, February 1997).
Here I give the announced list of books and survey papers that should give
a basis for understanding the current trends and needs in OP-SF.  Let me
say that the given list can be neither complete nor perfect. If somebody
feels that an important item is missing, please let me know.  The
following list should rather be understood as under construction.  We will
try to put this list on OP-SF Web, where it can easily be updated.
Electronically, the material could also be more easily organized in
various ways.

Readers who are interested in classical orthogonal polynomials should
probably first look at [Chihara], [NU], [Rainville], [Szego], or
[Tricomi]; readers looking for applications in mathematical physics might
consider [NU].

[Artin] Artin, E.: "The Gamma Function." Holt, Rinehart and Winston, New
York, 1964.

[Askey1] Askey, R. A. (Ed.): "Theory and Application of Special
Functions".  Proceedings of an advanced seminar sponsored by the
Mathematics Research Center, University of Wisconsin-Madison, March
21-April 2, 1975. Academic Press, New York, 1975.

[Askey2] Askey, R. A. (Ed.): "Orthogonal Polynomials and Special
Functions." Regional Conference Series in Applied Mathematics 21, SIAM,
Philadelphia, 1975.

[AKS] Askey, R. A., Koornwinder, T. H. and Schempp, W. (Eds.):  "Special
Functions: Group Theoretical Aspects and Applications." Mathematics and
Its Applications, Vol. 18. Reidel, Dordrecht-Boston-Lancaster, 1984.

[AW3] Askey, R. A. and Wilson, J.: Some basic hypergeometric orthogonal
polynomials that generalize Jacobi polynomials. Memoirs Amer. Math. Soc.
319, Providence, Rhode Island, 1985.

[Bailey] Bailey, W. N.:  "Generalized Hypergeometric Series". Cambridge
University Press, England, 1935;  reprinted 1964 by Stechert-Hafner
Service Agency, New York-London.

[Chihara] Chihara, T. S.: "An Introduction to Orthogonal Polynomials."
Gordon and Breach Publ., New York, 1978.

[Freud] Freud, G.: "Orthogonale Polynome". Birkhauser, Basel, 1969;
English translation, Pergamon Press, Oxford, 1971.

[GR] Gasper, G. and Rahman, M.: "Basic Hypergeometric Series."
Encyclopedia of Mathematics and Its Applications, Vol. 34.  Cambridge
University Press, 1990.

[Geronimus1] Geronimus, Ya. L.:  "Polynomials Orthogonal on a Circle and
Interval." International Series of Monographs on Pure and Applied
Mathematics, Vol. 18.  Pergamon Press, Oxford-London-New York-Paris, 1961.

[Geronimus2] Geronimus, Ya. L.:  Appendix to the Russian translation of
Szego's book "Orthogonal Polynomials." Staatsverlag fur
physikalisch-mathematische Literatur, Moskau, 1962.

[Henrici1] Henrici, P.: "Applied and Computational Complex Analysis, Vol. 1:
Power Series, Integration, Conformal Mapping, Location of Zeros."
John Wiley & Sons, New York, 1974.

[Henrici2] Henrici, P.: "Applied and Computational Complex Analysis, Vol.
2:  Special Functions, Integral Transforms, Asymptotics, Continued
Fractions." John Wiley & Sons, New York, 1977.

[Hua] Hua, L.K.: "Harmonic Analysis of Functions of Several Complex Variables
in the Classical Domains." Translations of Mathematical Monographs, Vol. 6,
Amer. Math. Soc., Providence, Rhode Island, 1963.

[Lebedev] Lebedev, N. N.:  "Special Functions and their Applications."
Translated and edited by Richard A. Silverman.  Dover Publications, New
York, 1972.

[LW] Lorentzen, L. and Waadeland, H.:  "Continued Fractions with
Applications." Studies in Computational Mathematics, Vol. 3.
North-Holland, Amsterdam, 1992.

[Miller1] Miller, W., Jr.: "Lie Theory and Special Functions." Academic
Press, New York, 1968.

[Miller2] Miller, W., Jr.: "Symmetry and Separation of Variables."
Encyclopedia of Mathematics and Its Applications, Vol. 4.
Addison-Wesley, Reading, Massachusetts, 1977.

[Nevai1] Nevai, P. G.:  "Orthogonal Polynomials." Memoirs Amer. Math.
Soc., Vol. 213, Providence, Rhode Island, 1979.

[Nevai2] Nevai, P. (Ed.): "Orthogonal Polynomials: Theory and Practice."
Proceedings of the NATO Advanced Study Institute on Orthogonal Polynomials
and Their Applications, Colombus, Ohio, U.S.A., May 22-June 3, 1989,
Kluwer Academic Publ., Dordrecht-Boston-London, 1990.

[NU] Nikiforov, A. F. and Uvarov, V. B.:  "Special Functions of
Mathematical Physics".  Translated from the Russian by R. P. Boas,
Birkhauser, Basel, 1988.

[NSU] Nikiforov, A. F., Suslov, S. K. and Uvarov, V. B.: "Classical
Orthogonal Polynomials of a Discrete Variable." Springer-Verlag,
Berlin-Heidelberg-New York, 1991.

[NS] Nikishin, E. M. and Sorokin, V. N.:  "Rational Approximations and
Orthogonality." Translations of Mathematical Monographs 92, Amer. Math.
Soc., Providence, Rhode Island, 1991.

[Olver] Olver, F. W. J.: "Asymptotics and Special Functions." Academic
Press, New York, 1974. (reprinted A. K. Peters, 1997)

[Perron] Perron, O.: "Die Lehre von den Kettenbruchen." Teubner, Leipzig,
1913; second edition, Chelsea, New York, 1950.

[PWZ] Petkovvsek, M., Wilf, H. S. and Zeilberger, D.:  "A=B." A. K.
Peters, Wellesley, 1996.

[Rainville] Rainville, E. D.: "Special Functions". The MacMillan Co., New
York, 1960.

[Richards] Richards, D. St. P. (Ed.):  "Hypergeometric Functions on
Domains of Positivity, Jack Polynomials, and Applications." Proceedings of
an AMS special session, March 22-23, 1991 in Tampa, FL, USA. Contemporary
Mathematics 138, Amer. Math. Soc., Providence, Rhode Island, 1992.

[Shohat] Shohat, J. A. and Tamarkin, J. D. : "The Problem of Moments."
Amer. Math. Soc., Providence, Rhode Island, 1963.

[Szego] Szego, G.: "Orthogonal Polynomials." Amer. Math. Soc. Coll.
Publ., Vol. 23, New York, 1939;  4th Edition, 1975.

[ST] Stahl, H. and Totik, V.:  "General Orthogonal Polynomials."
Encyclopedia of Mathematics and Its Applications.  Cambridge University
Press, Cambridge, 1992.

[Talman] Talman, J.: "Special Functions: a Group Theoretic Approach." W.
A. Benjamin, New York, 1968.

[Temme] Temme, N. M.: "Special Functions. An Introduction to the Classical
Functions of Mathematical Physics." John Wiley & Sons Inc., New York,

[Tricomi] Tricomi, F. G.: "Vorlesungen uber Orthogonalreihen."
Grundlehren der Mathematischen Wissenschaften 76, Springer-Verlag,
Berlin-Gottingen-Heidelberg, 1955.

[VanAssche] Van Assche, W.:  "Asymptotics for Orthogonal Polynomials."
Lecture Notes Math. 1265, Springer, Berlin-Heidelberg-New York, 1987.

[Vilenkin1] Vilenkin, N. Ya.:  "Special Functions and the Theory of Group
Representations."  Translations of Mathematical Monographs 22, Amer.
Math.  Soc., Providence, Rhode Island, 1968.

[Vilenkin2] Vilenkin, N. Ya., and Klimyk, A. U.:  "Representation of Lie
Groups and Special Functions, Vols. 1-3, and "Recent Advances", Kluwer
Academic Publ., Dordrecht-Boston-London, 1992-1995.

[Wall] Wall, H. S.: "Analytic Theory of Continued Fractions."  Chelsea,
Bronx, NY, 1973.

The following are handbooks and other reference manuals for
orthogonal polynomials and special functions.

[AS] Abramowitz, M. and Stegun, I. A.: "Handbook of Mathematical
Functions." Dover Publ., New York, 1964.

[Erdelyi1] Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.:
"Higher Transcendental Functions, Vols. 1-3."  McGraw-Hill, New York,

[Erdelyi1] Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.:
"Tables of Integral Transforms, Vols. 1-2."  McGraw-Hill, New York, 1954.

[GR] Gradshteyn, I. S. and Ryzhik, I. M.: "Table of Integrals, Series,
and Products."  Printed and CD-ROM Version.  Academic Press, San Diego,
California, 1996.

[Han] Hansen, E. R.: "A Table of Series and Products." Prentice-Hall,
Englewood Cliffs, NJ, 1975.

[Swarttouw] Koekoek, R. and Swarttouw, R. F.: "The Askey-scheme of
hypergeometric orthogonal polynomials and its q analogue." Report 94-05,
Technische Universiteit Delft, Faculty of Technical Mathematics and
Informatics, Delft, 1994.  Electronic version:

[MOS] Magnus, W., Oberhettinger, F. and Soni, R. P.:  "Formulas and
Theorems for the Special Functions of Mathematical Physics".  Springer,
Berlin-Heidelberg-New York, 1966.

[PBM] Prudnikov, A.P., Brychkov, Yu.A. and Marichev, O.I.:  "Integrals and
Series, Vols.1-3."  Gordon and Breach Publ., New York, 1989-1990.

Electronic Services

Here is a list of electronic services and WWW sites which are of interest
to the members of our Activity Group.

SIAM Activity Group on Orthogonal Polynomials and Special Functions.

Martin Muldoon and Tom H. Koornwinder: A collection of electronic services
relevant for OPSF

Hans Haubold: OPSF ftp site

Mathematical Reviews: about MathSciNet

Mathematical Reviews: MathSciNet

Mathematical Reviews: Author Lookup

Zentralblatt fur Mathematik: MATH Database 1931-1996 on-line

AMS: Preprint Server

Netlib: collection of mathematical software, papers, and databases

Elsevier: The CPC International Program Library

Rene Swarttouw: Electronic version of the Askey-Wilson scheme report.

Rene Swarttouw: An interactive on-line version of the Askey-Wilson scheme,
using Koepf's Maple implementations of Zeilberger's algorithm

Wolfram Research: On-line Mathematica Integrator

CECM: Inverse Symbolic Calculator

N. J. A. Sloane: Integer Sequences

Richard Fateman: Table of Integrals Look Up

Steven Finch: Favorite Mathematical Constants

David H. Bailey and Simon Plouffe: Recognizing Numerical Constants

Mathematics Archives: Numbers

Daniel Lozier: Numerical Evaluation of Special Functions

Wolfram Koepf

Topic #13  --------------  OP-SF NET 4.2 --------------- March 15, 1997
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.  Very recently, Hans Haubold has
constructed a convenient WWW interface for this ftp site, at the address


Via this home page you can move to a page listing all available files in
alphabetical order of authors, and offering a link to each file.  You can
also move from the home page to the ftp interface.  At the moment it is
only in this way that you can reach the submissions directory, where the
most recent contributions reside.

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 January 15, 1997 the following paper has been submitted to the

W. Koepf and D. Schmersau, Representations of Orthogonal
(see siam/submissions/koepf_schmersau6.ps).

Topic #14 --------------   OP-SF NET 4.2  ------------- March 15,1997
From: OP-SF Net Editors <thk@wins.uva.nl>, <muldoon@yorku.ca>
Subject: Changes of Address, WWW Pages, etc.

1. The preprint archive "Orthogonal polynomials and related special
functions"  maintained by Hans Haubold has got a new WWW address:


See Topic #13 for more information on this archive.

2. The URL for AT-NET should be changed to:

3. A particularly extensive list of Mathematical links is maintained at:
Mathematics Information Servers --- Penn State

4. Daniel Loeb has moved from Universite de Bordeaux, France to
a position at Daniel H. Wagner, Associates, Malvern, PA, USA.
His present address is:

171 Stoneway Lane, Bala Cynwyd, PA 19004-3124, USA
Phone +1-610-668-7732, Fax: +1-610-644-6293,
email: loeb@sprynet.com or loeb@pa.wagner.com

His Web site remains in Bordeaux but the address has changed slightly:

WWW: http://dept-info.labri.u-bordeaux.fr/~loeb/index.html

Topic #15  --------------  OP-SF NET 4.2 --------------- March 15, 1997
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 4.3 should reach the email address
poly@siam.org before May 1, 1997.

The Activity Group also sponsors a (printed) Newsletter edited by Wolfram
Koepf. Deadline for submissions to be included in the June 1997 issue is
May 15, 1997 and for the October 1997 issue it is September 15, 1997.

Please send your Newsletter contributions directly to the Editor:

Wolfram Koepf
Takustr. 7
D-14195 Berlin-Dahlem, Germany
tel.: +49-30-841 85-348/347
fax:  +49-30-841 85-269/125
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   -
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-            pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir -
-  WWW home page of this Activity Group:                              -
-           http://www.math.yorku.ca/Who/Faculty/Muldoon/siamopsf/    -
-  Information on joining SIAM                                        -
-      and this activity group:  service@siam.org                     -
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-      The elected Officers of the Activity Group are:                -
-              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                       -
-              Martin Muldoon, Webmaster and OP-SF Net editor         -
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