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- December 29, 1994 -
- O P - S F N E T Volume 1, Number 9 -
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- Tom H. Koornwinder, Editor thk@fwi.uva.nl -
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- The Electronic News Net of the SIAM Activity Group -
- on Orthogonal Polynomials and Special Functions -
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- Please send contributions to: poly@siam.org -
- & address changes to: poly-request@siam.org -
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Today's Topics:
1. Orthogonal polynomials and special functions in BAMS, January, 1995
2. In Memoriam P.J. de Doelder
3. Pictures wanted
4. First Maghrebian Colloquium on Analysis
5. New Maple package: summation
6. Urgent research question
7. Call for conjectures to be tested by undergraduate students
8. New errata for the book Basic hypergeometric series
9. Changes of address
10. WWW server for Journal of Approximation Theory
11. hep-th and q-alg archives
12. Recent additions to ftp site on orthogonal polynomials and
related special functions
13. Obtaining back issues and contributing to future issues of OP-SF Net
and the Newsletter
Calendar of events: see issue/topic:
1995
January 8-12: Conference on Approximation Theory, College Station, 1.4 #7
January 16-27: Conference on Exponential Asymptotics, Cambridge, UK 1.8 #11
March 17-18: Session "Approximation Theory and Special Functions" 1.7 #6
March 20-22: Stieltjes Colloquium in Toulouse 1.7 #7
May 29-June 2: Formal Power Series and Combinatorics, Paris 1.8 #13
June 9-10: Lee Lorch Conference 1995 1.7 #8
June 12-23: Fields Institute program on Special functions etc. 1.7 #9
July 3-7: Minisymposium at ICIAM '95, Hamburg:
"Orthogonal Polynomials and Spectral Methods" 1.8 #16
July 19-21: First Maghrebian Colloquium on Analysis 1.9 #4
Topic #1 -------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: Dick Askey
Subject: Orthogonal polynomials and special functions in BAMS, January, 1995
Orthogonal polynomials and special functions in Bull. Amer. Math. Soc.,
January, 1995.
The survey paper in this issue is "How many zeros of a random
polynomial are real?" by Alan Edelman and Eric Kostlan. In the
paper a tridiagonal matrix is given, what is now called the Kac
matrix. This is an (n+1)x(n+1) matrix with zeros on the main
diagonal, the integers 1,2,...,n below the main diagonal and
this sequence backwards above the main diagonal, with the
sequences starting in the upper left. The eigenvalues are
-n,-n+2,-n+4,...,n-2,n. A reference for this and the history
is given to a paper by John Todd and Olga Tausky in Linear Algebra
Appl. 150 (1991), 341-360. In fact, this matrix appeared much earlier
than in Mark Kac's nice paper "Random walk and the theory of Brownian
motion", Amer. Math. Monthly 54 (1947), 369-391. It comes from the
symmetric Krawtchouk polynomials, and the fact that the eigenvalues
are the integers above is just a reflection of the location of the
point masses for the Krawtchouk polynomial orthogonality. This
is usually given as the integers 0,1,...,n, but when the distribution
is symmetric there is a case for having the symmetry about x=0,
which is what was done here. There are many other such matrices.
The most general one coming from classical type orthogonal polynomials
comes from the q-Racah polynomials, and was treated by Askey and
Wilson in SIAM J. Math. Anal. 10 (1979), 1008-1016. Kac's Monthly
paper can be completely rewritten using orthogonality of symmetric
Krawtchouk polynomials to obtain his main results. Mark Kac
loved orthogonal polynomials, and once told me that he learned
the theorem we attribute to Favard in a book by Wintner, published
in 1929. However, I don't think he knew about Krawtchouk polynomials
when he died and so was not aware that his Monthly paper could be
redone in an easier way.
The book review of Deligne and Mostow's book "Commensurabilities
among lattices in PU(1,n)" written by Cohen and Hirzebruch is worth
reading whether you read the book or not. It may even be more
important for most of us to read if we are going to read the book,
for the essential connection with hypergeometric functions in
one and several variables is spelled out very nicely in the review.
I would appreciate other references to uses of special functions
in the published literature. This could be a use of our newsletter.
Topic #2 -------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: J. Boersma
Subject: In Memoriam P.J. de Doelder
In OP-SF Net 1.8, topic #7 it was already briefly mentioned that
P.J. de Doelder died on October 16, 1994. J. Boersma sent us the following.
In memoriam P.J. de Doelder
Pieter J. de Doelder, retired from Eindhoven University of Technology,
died on October 16, 1994 at the age of 75 years. From 1957 till 1982
de Doelder was a faculty member of the Department of Mathematics of
EUT, where he was primarily involved in teaching. In addition, de
Doelder was a prolific problem solver, particularly in the field of
special functions. Till the end of his life he made numerous
contributions to the Problem Sections of Nieuw Archief voor Wiskunde,
SIAM Review, and of the OP-SF Newsletter.
Topic #3 -------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: Eugene Tomer
Subject: Pictures wanted
If you happen to be at a meeting somewhere, or even if you don't, you
might carry along your photographic apparatus and take a few pictures.
The Newsletter of our Activity Group will print them so your friends
can see you have actually been there, or somewhere. See the last section
of the Newsletter on how to contribute photographic material.
Topic #4 -------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: A. Bakali
Subject: First Maghrebian Colloquium on Analysis
The first "Maghrebian Colloquium on Analysis" will be held in
Kenitra, Morocco during July 19-21, 1995. It is the intention that
such a colloquium will be organized yearly in one of the countries of
the Maghreb region. The next one will be held in Tunisia. It is open
to mathematicians from all countries. The fields of interest of this
first meeting are:
I) Harmonic Analysis
II) Functional Analysis and Applications
III) Potential Theory and Probability Theory
More particular attention will be paid to the following topics:
Representation theory, Spherical and special functions, Gelfand pairs
and their generalizations, Hypergroups, Operator theory and applied
functional analysis, Potential theory and Probability theory.
The working languages will be English and French.
The meeting will include plenary lectures and short communications in the
three parallel sessions I), II) and III).
If you are interested in participating, please contact prof. Bakali as
soon as possible at the address below, and mention if you want to give
a lecture (plenary or short communication).
A. Bakali
Equipe d'Analyse
Departement de Mathematiques et d'Informatique
Faculte des Sciences
Universite Ibn Tofail
BP 133, Kenitra
Morocco
fax: +212-7-37 27 70
Topic #5 -------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: Wolfram Koepf
Subject: New Maple package: summation
Maple package: summation
Authors: Wolfram Koepf and Gregor St\"olting
email: koepf@zib-berlin.de
Date: December 1994
This package is an implementation of the Gosper and Zeilberger
algorithms for indefinite and definite summation covering extensions
given by Koepf. The program is done on the lines of Tom Koornwinder's
program zeilb.
References:
[1] R. W. Gosper, Jr.:
Decision procedure for indefinite hypergeometric summation,
Proc. Nat. Acad. Sci. USA 75 (1978), 40-42.
[2] T. H. Koornwinder:
On Zeilberger's algorithm and
its q-analogue: a rigorous description.
J. of Comput. and Appl. Math. 48 (1993), 91-111.
[3] D. Zeilberger,
A fast algorithm for proving terminating hypergeometric identities,
Discrete Math. 80 (1990), 207-211.
The extensions are described in
[4] W. Koepf:
Algorithms for the indefinite and definite summation.
Konrad-Zuse-Zentrum Berlin (ZIB), Preprint SC 94-33 (Dezember 1994).
(see /ftp/pub/koepf/summation.tex or summation.ps in W. Al-Salam's archive,
ftp euler.math.ualberta.ca)
The package comes with a test file summation.tst including many examples.
Topic #6 -------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: Ernst Davidovich Krupnikov
Subject: Urgent research question
Dear colleagues:
who knows if anything has been done on generalizations
of summation theorems of Bailey and Whipple, Gauss (second) and Watson,
Kummer and Dixon?
Please email me corresponding references on this topic.
Ernst Davidovich Krupnikov
email: ernst@net.neic.nsk.su
Topic #7 -------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: Alan Schwartz
Subject: Call for conjectures to be tested by undergraduate students
William C. Connett and Alan L. Schwartz are using NSF funding to
organize a computational laboratory for undergraduate students. A
typical activity to test mathematical conjectures about orthogonal
polynomials and other special functions. We would like to share this
resource widely and we seek problems for these students to work on.
Currently students are using Maple to look at positivity of
linearization coefficents and to answer questions about the maximum of
certain specific families of polynomials.
If you would like to submit conjectures or if you have questions please
contact
Alan L. Schwartz or William C. Connett
schwartz@arch.umsl.edu connett@umslvma.bitnet
(314) 553-6719 (314) 553-6343
Department of Mathematics and Computer Science
University of Missouri - St. Louis
St. Louis, MO 63121
There will be a few summer research assistantships for
undergraduates to participate in this program. Interested students
should send inquiries to the address above (snailmail or email)
Topic #8 -------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: George Gasper
Subject: New errata for the book Basic hypergeometric series
Errata, updates of the References, etc.,
(as of Dec. 27, 1994) for the book
Basic Hypergeometric Series, by George Gasper and Mizan Rahman,
Encyclopedia of Mathematics and its Applications, Vol. 35,
Cambridge University Press, Cambridge-New York, 1990
are now available on file from George Gasper
(and probably soon also as file /ftp/pub/gasper-rahman.tex in W. Al-Salam's
archive, ftp euler.math.ualberta.ca).
Below are the errata added to the list since November 19, 1993:
p. 212, eq. (8.7.13): Insert the factor `` $(q; q)_s$ '' into the
denominator on the right side of the equation.
p. 191, Ex. 7.32 (ii): Insert the factor `` $q^{(\alpha - \beta) n/2}$ ''
after the `` $(-1)^n$ '' factor on the right side of the equation.
p. 275: In Wilson [1978] change ``polynomials'' to ``functions'' .
p. 167, eq. (7.3.13): Replace the factor $(-ac)^n$ by $(-acq^2)^{-n}$ .
Topic #9 -------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: OP-SF Net Editor
Subject: Changes of address
Eric Opdam (University of Leiden) will stay during January-June 1995 at:
University of Michigan, Math. Dept.
Ann Arbor, MI 48109-1003
USA
Marcel de Jeu, who recently got his Ph.D at the University of Leiden
and who is, like Eric Opdam, a specialist in the area of special
functions associated with root systems, will stay during 15 January -
15 July 1995 as a postdoc at:
MIT, Dept. of Math.
Cambridge, MA 02139
USA
Topic #10 ------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: Paul Nevai
Subject: WWW server for Journal of Approximation Theory
It is our pleasure to announce the establishment of a WWW server for
Journal of Approximation Theory at:
http://math.ohio-state.edu/Groups/JAT
This home page for JAT, still in development, contains large, easily
usable address and e-mail lists of people in Approximation Theory, as
well as tables of contents and additional information for authors and
readers of JAT.
Sincerely,
Paul Nevai and Allan Pinkus
Editors-in-Chiefs
J. Approx. Theory
Topic #11 ------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: Net Editor
Subject: hep-th and q-alg archives
The hep-th electronic archive contains preprints in the area of
theoretical high energy physics (string, conformal and field theory).
A lot of material involving special functions and orthogonal
polynomials can be found there, in particular quantum groups related
q-stuff. Since last week, new q-algebra preprints are being redirected
to a new archive q-alg (quantum algebra including knot theory).
The email and WWW addresses of the two sites are as follows:
hep-th: email: hep-th@xxx.lanl.gov or hep-th@babbage.sissa.it
WWW: http://xxx.lanl.gov/hep-th
q-alg: email: q-alg@eprints.math.duke.edu
WWW: http://www.msri.org/preprints
Send an email message to one of the two sites and put the word "help"
on the subject line if you want to receive more information.
Topic #12 ------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: Waleed A. Al-Salam
Subject: Recent additions to ftp site on orthogonal polynomials and
related special functions
Waleed Al-Salam has an anonymous ftp site at
euler.math.ualberta.ca
on orthogonal polynomials and related special functions.
It can also be accessed by using World Wide Web (xmosaic or Mosaic)
at the address ftp://euler.math.ualberta.ca.
Manuscripts can be obtained from directory pub and subdirectories.
In particular, examine the CONTENTS file in the pub directory.
If you wish to receive periodic info regarding recent additions to
this database please send an email message to
waleed@euler.math.ualberta.ca with your e-mail address.
You are invited to submit one or more of your not-yet-in-print
manuscripts which you wish to make available to the general OPS
community. They should be in Plain TeX, LaTeX, AMSTeX or AMSLaTeX
format. These manuscripts can be submitted by one of the following
methods:
a) E-mail to waleed@EULER.MATH.UALBERTA.CA
b) anonymous ftp to euler.math.ualberta.ca
then "cd submissions"
and finally "put file" where "file" is the name of the file
you wish to deposit.
Between November 11 and December 27, 1994 the following additions were
put in the pub directory:
M. L. Glasser, The quadratic formula made hard, a less radical approach
to solving equations. (see /ftp/pub/glasser.tex)
V. B. Kuznetsov, 3F2(1) hypergeometric function and quadratic R-matrix
algebra. (see /ftp/pub/kuznetsov_QISM2_hahn.tex)
T. H. Koornwinder, Special functions associated with rootsystems:
recent progress. (see /ftp/pub/koornwinder4.ps)
D. P. Gupta and D. Masson, Contiguous relations, continued fractions
and orthogonality: an 8phi7 model. (see /ftp/pub/massonc.tex)
V. Kowalenko and M.L. Glasser, Extensions and results from a method for
evaluating fractional integrals. (see /ftp/pub/glasser/glasser4.tex+
revtex sty files)
P. G. A. Floris, Addition formula for q-disk polynomials.
(see /ftp/pub/floris1.tex)
P. G. A. Floris, A noncommutative discrete hypergroup associated with
q-disk polynomials. (see /ftp/pub/floris2.tex)
R. Askey, M. Rahman and S. Suslov, On a general q-Fourier transformation
with non-symmetric kernel. (see /ftp/pub/askey-rahman-suslov.tex).
P. I. Etingof and A. A. Kirillov, Representation-theoretic proof of the
inner product and symmetry identities for Macdonald's polynomials.
(see /ftp/pub/ident.ps ).
H. T. Koelink, Addition formula for 2-parameter family of Askey-Wilson
polynomials (see /ftp/pub/koelink4.tex).
W. Koepf, Algorithms for the indefinite and definite summation.
(see /ftp/pub/koepf/summation.tex or summation.ps)
W. Koepf, Reduce package for the indefinite and definite summation.
(see /ftp/pub/koepf/sumreduce.tex or sumreduce.ps)
W. Koepf, Algebraische Darstellung tranzendenter Funktionen.
(see /ftp/pub/koepf/tranz.tex or tranz.ps)
H. T. Koelink and J. Verding, Spectral analysis and the Haar functional
on the quantum SU(2) group. (see /ftp/pub/koelink-verding.tex)
Topic #13 -------------- OP-SF NET --------------- December 29, 1994
~~~~~~~~~
From: Tom H. Koornwinder
Subject: Obtaining back issues and contributing to future issues of OP-SF Net
and the Newsletter
Back issues of OP-SF Net can be obtained from
ftp: ae.siam.org, in directory pub/opsf-net .
or gopher: gopher.siam.org
or WWW: gopher://gopher.siam.org
Contributions to the OP-SF Net 2.1 should reach the email
address poly@siam.org before February 1, 1995.
Contributions to the Spring issue of the Orthogonal Polynomials and
Special Functions Newsletter should reach the Editor Eugene Tomer
before February 10, 1995.
Items for the Newsletter without mathematical symbols can be submitted
in any convenient form, for example as a textfile or as a typewritten
manuscript. Items containing substantial mathematical symbols must be
submitted as a standard Latex file by e-mail or by disc. There is only
one exception: plain TeX files can be accepted by making special
arrangements with the Editor. AmsTeX and AmsLatex files cannot be
accepted. Whatever the content of your Latex article, you must use a
certain preamble which can be obtained by e-mail from the Editor.
Eugene Tomer
Applied Mathematics & Computing
150 Hernandez Avenue
San Francisco, CA 94127, USA
fax +1-415-731 3551
Contributions to either the Net or to the Newsletter will be
automatically considered also for inclusion in the other medium.
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- Special Functions and Orthogonal Polynomials. -
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- special functions and orthogonal polynomials community. This -
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- software, electronic archives, research questions, job openings. -
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- George Gasper, Vice Chair -
- Tom H. Koornwinder, Secretary and OP-SF Net Editor -
- Martin E. Muldoon, Program Director -
- Eugene Tomer, Newsletter Editor -
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