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May 15, 2003
O P - S F N E T Volume 10, Number 3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Editor:
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
Subscribe by mailing to: poly-request@siam.org
or to: listproc@nist.gov
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Today's Topics:
1. Alan Schwartz
2. Workshop dedicated to Dick Askey
3. Special Session on Classical and Nonlinear Special Functions
4. Roros Conference on Orthogonal Functions and Related Topics
5. ISAAC 2003
6. CAOP moved
7. Small gaps between prime numbers
8. New book by I. G. Macdonald
9. New Book on Basic Fourier Series
10. Preprints in xxx Archive
11. About the Activity Group
12. Submitting contributions to OP-SF NET and Newsletter
Calendar of Events:
2003
June 8-12: AMS-IMS-SIAM Summer Research Conference "Spectral theory
and inverse spectral theory for Jacobi operators",
Snowbird, Utah, USA 10.1 #1
June 16-20: SIAM Annual Meeting, Montreal, Canada
in conjunction with CAIMS 9.6 #2 10.2 #1
June 18-21: Special session on "Constructive Approximation Theory"
during the AMS-RSME Joint Meeting, Seville, Spain 9.4 #4
July 7-11: 5th International Congress on Industrial and Applied
Mathematics, ICIAM 2003, Sydney, Australia. 8.6 #6
July 14-26: Summer school on "Orthogonal Polynomials and
Special Functions", Coimbra, Portugal 10.1 #2
August 11-16: Fourth ISAAC Congress, Toronto, Canada 9.2 #6 9.4 #5
August 11-16: Conference on Orthogonal Functions and
Related Topics, Roros, Norway 10.1 #3
August 18-22: Seventh International Symposium on Orthogonal
Polynomials, Special Functions and Applications,
Copenhagen, Denmark 8.6 #7 9.4 #6 10.1 #4 10.2 #2
August 25-27: Special Functions, Representation Theory and
Applications, Meeting in honour of Tom Koornwinder,
Amsterdam 9.6 #3 10.2 #3
September 15-19: Sturm Colloquium, Geneva, Switzerland 10.2 #4
October 18-22: International Workshop on Special Functions,
Orthogonal Polynomials, Quantum Groups and Related Topics
dedicated to Dick Askey's 70th birthday, Bexbach, Germany 10.3 #2
2004
January 7-10: Joint Mathematics Meetings, Phoenix, Arizona, USA
(including Special Sessions on "Classical and Nonlinear
Special Functions" and on "Theory and Applications of
Orthogonal Polynomials") 10.3 #3
Future Plans:
Dan Lozier (OP-SF NET 9.4, Topic #2) suggests a SIAM-sponsored meeting in
Orthogonal Polynomials and Special Functions to be held in Washington, DC.
Present planning suggests a date in summer 2005.
Topic #1 ------------ OP-SF NET 10.3 ------------- May 15, 2003
~~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Alan Schwartz
Earlier this year, William Connett circulated
the following message:
"Friends:
I wanted to let you know that Alan Schwartz died on
January 2, after a long and painful illness. As many of you know
this illness caused him to retire from the university early last
year, and he moved to Washington D.C. to be near his children and
grandchildren. He had been ill for so long that I had begun to
feel this was the normal state of affairs, and was surprised by
the sudden end. Given the increasing difficulties of his life,
though, I guess that the quick end is better than the
alternatives. He was a good mathematician, and a great friend, I
will miss him very much.
Wm. Connett"
We hope that it will be possible to publish a longer notice on Alan
Schwartz in a future issue.
Topic #2 ------------ OP-SF NET 10.3 ------------- May 15, 2003
~~~~~~~~~~~~~~
From: Jasper Stokman
Subject: Workshop dedicated to Dick Askey
Currently I am organizing together with Sergei Suslov, Andreas Ruffing,
Tom Koornwinder and Erik Koelink an international workshop on special
functions, orthogonal polynomials, quantum groups and related topics
(dedicated to Dick Askey on his 70th birthday) in Bexbach, Germany,
18-22 October 2003.
This meeting is organized in cooperation with the Copenhagen meeting,
18-22 August, 2003 and Amsterdam meeting, 25-27 August 2003
International Organizing Committee:
Erik Koelink, Tom Koornwinder, Jasper Stokman,
Andreas Ruffing, Sergei Suslov
Local Organizing Committee:
Andreas Ruffing (Chair), Kristine Ey,
Clemens Lindemann (President of Saarpfalz District),
Heinz Mueller (Mayor of the Town of Bexbach)
Location: Hotel Hochwiesmuehle, Bexbach, Germany
Topics include the areas of research influenced by Dick Askey - among
them: Classical orthogonal polynomials: Askey-Wilson polynomials and
their special and/or limiting cases, biorthogonal rational functions,
integral transforms including q-Fourier transform and Askey-Wilson
function transform, q-Fourier series, Askey-Wilson operators and their
inverses, quantum groups and special functions, q-harmonic oscillators,
and others.
About 30 participants will be invited to present 30 min talks. In
addition, the program will give the participants a possibility to work
together on ongoing research projects. Due to the space limitation and
limiting funding participation is by invitation from the organizers
only.
More information can be found on the workshop homepage at
http://hahn.la.asu.edu/~suslov/bexbach/index.html
Topic #3 ------------ OP-SF NET 10.3 ------------- May 15, 2003
~~~~~~~~~~~~~~
From: Pete McCoy
Subject: Special Session on Classical and Nonlinear Special Functions
The SIAM Activity Group on Orthogonal Polynomials and Special Functions
will be co-hosting a joint AMS-SIAM Special Session on
"Classical and Nonlinear Special Functions and their Applications"
to be held at the Joint Mathematics Meetings, Phoenix, Arizona, during
the period January 7-10, 2004. The session will be organized by Peter A.
Clarkson (University of Kent), Francisco Marcellan (Universidad Carlos
III) and Pete McCoy (U.S. Naval Academy)
Abstract:
The theme of this session is special functions, including both classical
special functions, the Painleve equations, and applications of these
functions.
Special functions provide important analytical tools in the
physical sciences, engineering and statistics as well as in pure
and applied mathematics. They also play a role in mathematical
modeling and simulation. A large project to create a new handbook
and Web site, sponsored by NIST and NSF, has focused attention on
the mathematical properties of these functions. As a result, the
functions and their properties have been organized, and some
research questions have been exposed. Some of the talks in this
session are related to the NIST/NSF project, while others are
devoted to representative applications of special functions and to
recent work in nonlinear special functions, especially the
Painleve transcendents.
The Painleve equations are six second order, nonlinear ordinary
differential equations which have arisen in a variety of physical
applications and also as symmetry reductions of soliton equations. They
may be thought of as nonlinear special functions. Further the Painleve
equations arise in a wide variety of important applications including
asymptotics of nonlinear evolution equations, statistical mechanics,
plasma physics, nonlinear waves, G\"ortler vortices in boundary layers,
Hele-Shaw problems, polyelectrolytes and electrolysis, Bose-Einstein
condensation, quantum gravity and quantum field theory, general
relativity, nonlinear optics and fibre optics as well as links to other
areas of Mathematics including combinatorics, orthogonal polynomials,
random matrices and special functions.
The program complete program of speakers will follow in a later issue
of OP-SF NET.
Information on the Joint Meetings is available at:
http://www.ams.org/amsmtgs/2078_intro.html
Editor's Note: The Program for the Joint Meetings also includes a
Special Session "Theory and Applications of Orthogonal Polynomials" to
be organized by Mourad Ismail and Barry Simon.
Topic #4 ------------ OP-SF NET 10.3 ------------- May 15, 2003
~~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Roros Conference on Orthogonal Functions and Related Topics
OP-SF Net 10.1, Topic #3, had the announcement of a conference on
Orthogonal Functions and Related Topics to be held in Roros, Norway,
August 11-16, 2003 in Honour of the 70th Birthday of Olav Njastad.
Fuller information is available at the conference web site:
http://www.alt.hist.no/~froder/corfu/
Topic #5 ------------ OP-SF NET 10.3 ------------- May 15, 2003
~~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: ISAAC 2003
As announced in OP-SF NET 9.2, Topic #6 and OP-SF NET 9.4, Topic #5 the
Fourth ISAAC Congress will be held in Toronto, Canada during August
11-16, 2003. Further information about the ISAAC Congress can be found
at
http://www.math.yorku.ca/isaac03/
The program includes a plenary talk "Determinants and Orthogonal
Polynomials" by Richard Askey on August 11. On August 11-12 there will
be a special session on Orthogonal Polynomials and Special Functions
organized by Martin Muldoon. Confirmed speakers include Victor Adamchik,
Joaquin Bustoz, William Connett, Mark Defazio, Dmitrii B. Karp, Lee
Lorch and Roderick Wong.
Topic #6 ------------ OP-SF NET 10.3 ------------- May 15, 2003
~~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: CAOP moved
CAOP is a package for calculating formulas by Maple for orthogonal
polynomials belonging to the Askey scheme. It was developed by Rene
Swarttouw and it is currently maintained by Tom Koornwinder, in
collaboration with Wolfram Koepf and Rene Swarttouw, and with technical
assistance by Andre Heck. See OP-SF NET 8.6 #14 for the previous message
about CAOP.
The address of the web page of CAOP has recently changed. It
can now be reached on
http://amstel.science.uva.nl:7090/CAOP/
Topic #7 ------------ OP-SF NET 10.3 ------------- May 15, 2003
~~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: Small gaps between prime numbers
Recently the announcement by Dan Goldston and Cem Yildirim about a
dramatic improvement of estimates of small gaps between successive prime
numbers created a lot of excitement. By the way, a technical difficulty
in the proof has been discovered which for now remains unresolved, see
http://aimath.org/primegaps/
For readers of OP-SF NET it may be of interest that the original
technical description of the result on
http://aimath.org/primegaps/goldston_tech/
mentions the use of Laguerre polynomials in the proof:
Goldston's and Yildirim's approach begins with the methods of
Hardy-Littlewood and Bombieri-Davenport. They have discovered an
extraordinary way to approximate, on average, sums over prime
$k$-tuples. We believe, after work of Gallagher using the
Hardy-Littlewood conjectures for the distribution of prime $k$-tuples,
that the prime numbers in a short interval $[N, N+\lambda\log N]$ are
distributed like a Poisson random variable with parameter $\lambda$.
Goldston and Yildirim exploit this model in choosing approximations.
They ultimately use the theory of orthogonal polynomials to express the
optimal approximation in terms of the classical Laguerre polynomials.
Hardy and Littlewood could have proven this theorem under the assumption
of the Generalized Riemann Hypothesis; the Bombieri-Vinogradov theorem
allows for the unconditional treatment.
Topic #8 ------------ OP-SF NET 10.3 ------------- May 15, 2003
~~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: New book by I.G. Macdonald
Published in March 2003:
I.G. Macdonald,
Affine Hecke algebras and orthogonal polynomials,
Cambridge University Press, 2003,
186 pp., ISBN 0521824729, 35.00 pounds.
From
http://titles.cambridge.org/catalogue.asp?isbn=0521824729
we quote:
Contents:
Introduction; 1. Affine root systems; 2. The extended affine Weyl
group; 3. The braid group; 4. The affine Hecke algebra; 5. Orthogonal
polynomials; 6. The rank 1 case; Bibliography; Index.
In recent years there has developed a satisfactory and coherent theory
of orthogonal polynomials in several variables, attached to root
systems, and depending on two or more parameters. These polynomials
include as special cases: symmetric functions; zonal spherical functions
on real and p-adic reductive Lie groups; the Jacobi polynomials of
Heckman and Opdam; and the Askey-Wilson polynomials, which themselves
include as special or limiting cases all the classical families of
orthogonal polynomials in one variable. This first comprehensive and
organised account of the subject aims to provide a unified foundation
for this theory, to which the author has been a principal contributor.
It is an essentially self-contained treatment, accessible to graduate
students familiar with root systems and Weyl groups. The first four
chapters are preparatory to Chapter V, which is the heart of the book
and contains all the main results in full generality.
Topic #9 ------------ OP-SF NET 10.3 ------------- May 15, 2003
~~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: New Book on Basic Fourier Series
The following is from the web site:
http://hahn.la.asu.edu/~suslov/bfs/
An Introduction to Basic Fourier Series
by
Sergei K. Suslov
Arizona State University
Kluwer Academic Publishers
DORDRECHT / BOSTON / LONDON
DEVELOPMENTS IN MATHEMATICS, VOL. 9
ISBN 1-4020-1221-7
Dedicated to Dick Askey on his 70th birthday
This is an introductory volume on a novel theory of basic Fourier
series, a new interesting research area in classical analysis and
q-series. This research utilizes approximation theory, orthogonal
polynomials, analytic functions, and numerical methods to study the
branch of q-special functions dealing with basic analogs of Fourier
series and their applications. The present theory has interesting
applications and connections to general orthogonal basic hypergeometric
functions, a q-analog of zeta function, and, possibly, quantum groups
and mathematical physics.
Audience: Researchers and graduate students interested in recent
developments in q-special functions and their applications.
Contents:
Foreword
Preface
Chapter 1. Introduction
1.1. Some Basic Exponential Functions
1.2. Basic Fourier Series
1.3. About This Book
1.4. Exercises for Chapter 1
Chapter 2. Basic Exponential and Trigonometric Functions
2.1. Differential Equation for Harmonic Motion
2.2. Difference Analog of Equation for Harmonic Motion
2.3. Basic Exponential Functions
2.4. Basic Trigonometric Functions
2.5. q-Linear and Linear Grids
2.6. Exercises for Chapter 2
Chapter 3. Addition Theorems
3.1. Introduction
3.2. First Proof of Addition Theorem: Analytic Functions
3.3. Second Proof of Addition Theorem: Product Formula
3.4. Third Proof of Addition Theorem: Difference Equation
3.5. Another Addition Theorem
3.6. Addition Theorems on q-Linear and Linear Grids
3.7. Application: Continuous q-Hermite Polynomials
3.8. Exercises for Chapter 3
Chapter 4. Some Expansions and Integrals
4.1. Main Results
4.2. Proofs of (4.1.1)
4.3. Proofs of (4.1.3)
4.4. Orthogonality Property
4.5. Ismail and Zhang Formula
4.6. q-Exponentials and Connection Coefficient Problems
4.7. More Expansions and Integrals
4.8. Second Proof of Ismail, Rahman and Zhang Formula
4.9. Miscellaneous Results
4.10. Exercises for Chapter 4
Chapter 5. Introduction of Basic Fourier Series
5.1. Preliminaries
5.2. Orthogonality Property for q-Trigonometric Functions
5.3. Formal Limit q->1^-
5.4. Some Properties of Zeros
5.5. Evaluation of Some Constants
5.6. Orthogonality Relations for q-Exponential Functions
5.7. Basic Fourier Series
5.8. Some Basic Trigonometric Identities
5.9. Exercises for Chapter 5
Chapter 6. Investigation of Basic Fourier Series
6.1. Uniform Bounds
6.2. Completeness of Basic Trigonometric System
6.3. Asymptotics of Zeros
6.4. Pointwise Asymptotics of Basis
6.5. Bilinear Generating Functions
6.6. Methods of Summation of Basic Fourier Series
6.7. Basic Trigonometric System and q-Legendre Polynomials
6.8. Analytic Continuation of Basic Fourier Series
6.9. Miscellaneous Results
6.10. Exercises for Chapter 6
Chapter 7. Completeness of Basic Trigonometric System
7.1. Completeness in L^2 and q-Lommel Polynomials
7.2. Completeness in L^p: General Results
7.3. Example: Some Infinite Products
7.4. Example: Basic Sine and Cosine Functions
7.5. Example: Jackson's q-Bessel Functions
7.6. Exercises for Chapter 7
Chapter 8. Improved Asymptotics of Zeros
8.1. Interpretation of Zeros and Preliminary Results
8.2. Lagrange Inversion Formula
8.3. Asymptotics of k'(w) and k''(w)
8.4. Improved Asymptotics
8.5. Alternative Forms of c_2(q)
8.6. Monotonicity of c_1(q)
8.7. Exercises for Chapter 8
Chapter 9. Some Expansions in Basic Fourier Series
9.1. Expansions of Some Polynomials
9.2. Basic Sine and Cosine Functions
9.3. Basic Exponential Functions
9.4. Basic Cosecant and Cotangent Functions
9.5. Some Consequences of Parseval's Identity
9.6. More Expansions
9.7. Even More Expansions
9.8. Miscellaneous Results
9.9. Exercises for Chapter 9
Chapter 10. Basic Bernoulli and Euler Polynomials and Numbers and
q -Zeta Function
10.1. Bernoulli Polynomials, Numbers and Their q -Extensions
10.2. Some Properties of q-Bernoulli Polynomials
10.3. Extension of q-Bernoulli Polynomials
10.4. Basic Euler Polynomials and Numbers
10.5. Some Properties of q-Euler Polynomials
10.6. Extensions of Riemann Zeta Function and Related Functions
10.7. Analytic Continuation of q-Zeta Function
10.8. Exercises for Chapter 10
Chapter 11. Numerical Investigation of Basic Fourier Series
11.1. Eigenvalues
11.2. Euler-Rayleigh Method
11.3. Lower and Upper Bounds
11.4. Eigenfunctions
11.5. Some Examples of Basic Fourier Series and Related Sums
11.6. Exercises for Chapter 11
Chapter 12. Suggestions for Further Work
Appendix A. Selected Summation and Transformation Formulas and Integrals
A.1. Basic Hypergeometric Series
A.2. Selected Summation Formulas
A.3. Selected Transformation Formulas
A.4. Some Basic Integrals
Appendix B. Some Theorems of Complex Analysis
B.1. Entire Functions
B.2. Proof of Lagrange's Inversion Formula
B.3. Dirichlet Series
B.4. Asymptotics
Appendix.C. Tables of Zeros of Basic Sine and Cosine Functions
Appendix D. Numerical Examples of Improved Asymptotics
Appendix E. Numerical Examples of Euler-Rayleigh Method
Appendix F. Numerical Examples of Lower and Upper Bounds
Bibliography
Index
Your comments: sks@asu.edu
Topic #10 ------------ OP-SF NET 10.3 ------------- May 15, 2003
~~~~~~~~~~~~~~
From: OPSF NET Editor
Subject: Preprints in xxx Archive
The following preprints related to the fields of orthogonal polynomials
and special functions were recently posted or cross-listed to one of the
subcategories of the xxx archives. See especially:
http://front.math.ucdavis.edu/math.CA
http://front.math.ucdavis.edu/math.CO
http://front.math.ucdavis.edu/math.QA
http://xxx.lanl.gov/archive/solv-int
http://www.arXiv.org/abs/math.CO/0303025
Title: Sur une generalisation des coefficients binomiaux
Authors: F. Jouhet, B. Lass, J. Zeng
Comments: 14 pages
Subj-class: Combinatorics
http://www.arXiv.org/abs/math.CA/0303061
Title: On a hypergeometric identity of Gelfand, Graev and Retakh
Authors: Christian Krattenthaler (Université Claude Bernard Lyon-I),
Hjalmar Rosengren (Chalmers University of Technology and Göteborg
University)
Comments: considerably revised and extended; more $q$-analogues are
derived; in particular, a new section has been added with
$q$-analogues which are not only valid formally but also analytically
Subj-class: Classical Analysis and ODEs
MSC-class: 33C70 (Primary) 33C20 33D70 (Secondary)
http://www.arXiv.org/abs/math.NT/0303066
Title: Irrationalit\'e de valeurs de z\^eta (d'apr\`es Ap\'ery,
Rivoal, ...)
Authors: Stéphane Fischler
Comments: Bourbaki Seminar, November 2002 ; to appear in Ast\'erisque;
45 pages ; in French
Subj-class: Number Theory; Classical Analysis and ODEs; Combinatorics
MSC-class: 11J72 (Primary) 11G55, 11M06, 33C20, 41A21 (Secondary)
http://www.arXiv.org/abs/math.CA/0303093
Title: Multiple Wilson and Jacobi-Pineiro polynomials
Authors: B. Beckermann, J. Coussement, W. Van Assche
Comments: 22 pages, 2 figures
Subj-class: Classical Analysis and ODEs
MSC-class: 33C45; 42C05
http://www.arXiv.org/abs/math.CO/0303138
Title: Squaring the terms of an $\ell^{th}$ order linear recurrence
Authors: Toufik Mansour
Comments: 6 pages
Subj-class: Combinatorics
MSC-class: B39; 05A15
http://www.arXiv.org/abs/math.CO/0303147
Title: On operators on polynomials preserving real-rootedness and the
Neggers-Stanley Conjecture
Authors: Petter Brändén
Subj-class: Combinatorics; Classical Analysis and ODEs
MSC-class: 06A07;05E99;26C10
http://www.arXiv.org/abs/math.CO/0303149
Title: The generating function of two-stack sortable permutations by
descents is real-rooted
Authors: Petter Brändén
Comments: 4 pages
Subj-class: Combinatorics
MSC-class: 05A15;05A05;26C10
http://www.arXiv.org/abs/math.QA/0303178
Title: Hyperbolic beta integrals
Authors: Jasper V. Stokman
Comments: 35 pages
Subj-class: Quantum Algebra; Classical Analysis and ODEs
http://www.arXiv.org/abs/math.CA/0303204
Title: Theta hypergeometric series
Authors: V.P. Spiridonov
Comments: 19 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33Dxx, 33E20
Journal-ref: Proc. NATO ASI Asymptotic Combinatorics with Applications
to Mathematical Physics (St. Petersburg, July 9-22, 2001), Kluwer,
Dordrecht, 2002, pp. 307-327
http://www.arXiv.org/abs/math.CA/0303205
Title: Theta hypergeometric integrals
Authors: V.P. Spiridonov
Comments: 40 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33Dxx, 33E20, 39A13
http://www.arXiv.org/abs/math.CA/0303211
Title: A second addition formula for continuous q-ultraspherical
polynomials
Authors: Tom H. Koornwinder
Comments: 13 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33D45 (primary); 33D80 (secondary)
http://www.arXiv.org/abs/math.NT/0303250
Title: q-series and L-functions related to half-derivatives of the
Andrews--Gordon identity
Authors: Kazuhiro Hikami
Comments: 18 pages, related papers can be found from this http URL
Subj-class: Number Theory; Quantum Algebra; Mathematical Physics
http://www.arXiv.org/abs/math.CO/0303263
Title: Determinantal Construction of Orthogonal Polynomials Associated
with Root Systems
Authors: Jan Felipe van Diejen, Luc Lapointe, Jennifer Morse
Comments: 28 pages
Subj-class: Combinatorics; Quantum Algebra
MSC-class: 05E35
http://www.arxiv.org/abs/math.HO/0303267
Title: Trees, permutations and the tangent function
Authors: Ross Street
Comments: 9 pages, pdf file of MacWrite document
Subj-class: History and Overview; Combinatorics
MSC-class: 41A58
Journal-ref: Reflections 27 (2) (Math. Assoc. of New South Wales,
May 2002) 19-23
http://www.arXiv.org/abs/math-ph/0303016
Title: Hypergeometric solutions of some algebraic equations
Author: A.M. Perelomov
Comments: LaTeX, 16 pp
Subj-class: Mathematical Physics
http://www.arXiv.org/abs/nlin.SI/0303032
Title: _10E_9 solution to the elliptic Painlev'e equation
Authors: Kenji Kajiwara, Masatoshi Noumi, Tetsu Masuda,
Yasuhiro Ohta, Yasuhiko Yamada
Comments: 12 pages
Subj-class: Exactly Solvable and Integrable Systems; Quantum Algebra
http://www.arXiv.org/abs/math.CA/0304155
Title: Probabilistic aspects of Al-Salam-Chihara polynomials
Authors: Wlodzimierz Bryc, Wojciech Matysiak, Pawel J. Szablowski
Comments: LaTeX, 7 pages
Subj-class: Classical Analysis and ODEs
MSC-class: 33D45 (Primary) 05A30; 15A15; 42C05 (Secondary)
http://www.arXiv.org/abs/math.QA/0304189
Title: Elliptic U(2) quantum group and elliptic hypergeometric series
Authors: Erik Koelink, Yvette van Norden, Hjalmar Rosengren
Comments: 20 pages
Subj-class: Quantum Algebra; Representation Theory
http://www.arXiv.org/abs/math.CA/0304249
Title: Summations and transformations for multiple basic and elliptic
hypergeometric series by determinant evaluations
Authors: Hjalmar Rosengren, Michael Schlosser
Comments: 30 pages
Subj-class: Classical Analysis and ODEs; Combinatorics; Quantum Algebra
MSC-class: 33D67 (Primary) 05A30, 33D05 (Secondary)
http://www.arXiv.org/abs/math.CA/0304317
Title: An Entry of Ramanujan on Hypergeometric Series in his
Notebooks
Authors: K. Srinivasa Rao (The Institute of Mathematical Sciences,
Chennai), G. Vanden Berghe (Universiteit Gent),
Christian Krattenthaler (Université Claude Bernard Lyon-I)
Comments: 8 pages, AmS-LaTeX
Subj-class: Classical Analysis and ODEs
MSC-class: 33C20 (Primary) 33C05, 33B15 (Secondary)
http://www.arXiv.org/abs/math.RT/0304357
Title: Differential Recursion Relations for Laguerre Functions on
Hermitian Matrices
Authors: Mark Davidson, Gestur Olafsson
Subj-class: Representation Theory; Functional Analysis
MSC-class: 22E45, 33C52, 22F30, 43A10
http://www.arXiv.org/abs/math.FA/0304361
Title: A Paley-Wiener theorem for the $\Theta$-spherical transform:
the even multiplicity case
Authors: Gestur Olafsson, Angela Pasquale
Subj-class: Functional Analysis
MSC-class: 33C67, 43A90, 43A85
http://www.arXiv.org/abs/math.CA/0304381
Title: Some Rational Solutions to Painleve' VI
Authors: Gert Almkvist
Comments: 13 pages. LaTeX. Submitted to Canadian Journal of Mathematics
Subj-class: Classical Analysis and ODEs
MSC-class: 34A34
http://www.arXiv.org/abs/math.CA/0304382
Title: A Four-parametric Rational Solution to Painleve' VI
Authors: Gert Almkvist
Comments: 14 pages. LaTeX
Subj-class: Classical Analysis and ODEs
MSC-class: 34A34
http://www.arXiv.org/abs/math.QA/0304448
Title: q-Multiple Zeta Functions and q-Multiple Polylogarithms
Authors: Jianqiang Zhao
Comments: 20 pages
Subj-class: Quantum Algebra; Number Theory
MSC-class: 11M41; 81R50;11R42
http://www.arXiv.org/abs/math-ph/0304008
Title: Equilibrium of charges and differential equations solved by
polynomials
Authors: Igor Loutsenko
Comments: LATEX, 15 pages
Subj-class: Mathematical Physics; Complex Variables; Exactly Solvable and
Integrable Systems
http://www.arXiv.org/abs/math-ph/0304027
Title: On the expansion of the Kummer function in terms of incomplete
Gamma functions
Authors: Carlo Morosi (Politecnico di Milano), Livio Pizzocchero
(Universita' di Milano)
Comments: 21 pages, 6 figures. To appear in "Archives of Inequalities and
Applications"
Subj-class: Mathematical Physics; Classical Analysis and ODEs
MSC-class: 33C15, 41AXX
http://www.arXiv.org/abs/math-ph/0304041
Title: Exact, explicit and entire solutions to a nontrivial
finite-difference equation and their applications
Authors: M. Aunola
Comments: 1 page TeX plus Mathematica notebook. The TeX-file contains an
introductory summary. Explicit formulae are included as a ready-to-use
Mathematica notebook "Exactsolu.nb" which is included with this submission
(download and unpack the source). The expressions are simply too long
to be printed so only the leading terms will be included in
the manuscript to be submitted
Subj-class: Mathematical Physics
http://www.arXiv.org/abs/math-ph/0304042
Title: Affine Weyl group approach to Painlev\'e equations
Authors: Masatoshi Noumi
Subj-class: Mathematical Physics
MSC-class: 34M55, 39A12, 37K35
Journal-ref: Proceedings of the ICM, Beijing 2002, vol. 3, 497--510
Topic #11 ------------ OP-SF NET 10.3 ------------- May 15, 2003
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From: OP-SF NET Editor
Subject: About the Activity Group
The SIAM Activity Group on Orthogonal Polynomials and Special Functions
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Topic #12 ------------ OP-SF NET 10.3 ------------- May 15, 2003
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From: OP-SF NET Editor
Subject: Submitting contributions to OP-SF NET and Newsletter
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OP-SF NET is a forum of the SIAM Activity Group on
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Send submissions to: poly@siam.org
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The elected Officers of the Activity Group (2002-2004) are:
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Martin Muldoon, OP-SF NET editor
Bonita Saunders, Webmaster
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