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- JULY 15, 1996 -
- O P - S F N E T Volume 3, Number 4 -
- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -
- Editors: -
- Tom H. Koornwinder thk@fwi.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 Modern Topics in Orthogonal Systems
2. Business Meeting in Kansas City
3. Askey and Rota Lectures during Seattle Mathfest
4. Chokika (Hypergeometry) Festival in Kyushu
5. Centenary conference at University of Wisconsin - Madison
6. ISAAC Congress 1997
7. 9th International Conference on Formal Power Series
and Algebraic Combinatorics, Vienna, 1997.
8. Report on Umbral Calculus Workshop, MIT, April 1996
9. Report on Chebyshev Memorial Conference, Moscow, May 1996
10. Report on Workshop on Special Functions, Montreal, May 1996
11. Report on Special Functions Session, Antwerp, May 1996
12. A computer implementation of the Askey-Wilson scheme
13. Obituary: Lawrence C. Biedenharn, Jr.
14. Richard Askey on Waleed Al-Salam
15. Book Report (Feinsilver and Schott)
16. Call for Questions (undergraduate research)
17. Problem (Kontorovich-Lebedev transform)
18. Changes of Address, WWW pages. etc.
19. ftp site for papers in Orthogonal Polynomials and Special Functions
20. Obtaining back issues of OP-SF Net and submitting contributions
to OP-SF Net and Newsletter
Calendar of events: see issue/topic:
1996
July 15-20: International Colloquium on Group Theoretical Methods in
Physics, Goslar, Germany 3.1 #11
July 21-26: ICCAM 96, Leuven, Belgium 3.1 #12
July 22-26: SIAM Annual Meeting in Kansas City 3.2 #3 and 3.4 #2
July 23 and 26: Minisymposium on Modern Topics in Orthogonal Systems
at SIAM Annual Meeting in Kansas City 3.3 #1 and 3.4 #1
August 10-12: Lectures by Askey and Rota during Seattle Mathfest 3.4 #3
August 23-30: Workshop Transform Methods & Special Functions 2.6 #10
(Varna, Bulgaria)
September 1 - October 25: MSRI program on Enumeration and partially
ordered sets 3.3 #5
September 9-12: Chokika (Hypergeometry) Festival in Kyushu 3.4 #4
September 23-28: III International Conference on Functional Analysis
and Approximation Theory (Italy) 3.1 #13
1997
January 13-24: Workshop on Special Functions & Differential Equations,
Madras 3.3 #6
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 3.4 #6
June 24-28: Continued Fractions and Geometric Function Theory 3.2 #8
(Trondheim, Norway)
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 (e-mail: 8spoa@obelix.cica.es)
Topic #1 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Willard Miller, Jr.
Subject: Minisymposium on Modern Topics in Orthogonal Systems
As announced in OP-SF NET 3.3, Topic #1, SIAG/OS is sponsoring this
minisymposium at the 1996 SIAM Annual Meeting which will be held July 22-26,
1996 at the Hyatt Regency Crown Center, Kansas City, Missouri. We regret to
announce that the July 26 talk by Robert Gustafson on "Multivariate symmetric
orthogonal polynomials generalizing Jacobi polynomials and interpolation on
symmetric lattices in $R^n$" has been cancelled. The remaining part of the
program, including talks on "Wavelets" by Gilbert Walter, P. R. Massopust and
T. Q. Nguyen on Tuesday, July 23, 8:30 to 10:30 a.m. and the talk by Amos Ron
on Friday at 8:30 a.m. will go ahead as scheduled.
Topic #2 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Charles Dunkl
Subject: Business Meeting in Kansas City
Members of the Activity Group and other interested participants at the
SIAM Annual Meeting are invited to attend a short business meeting at 9:30
a.m. on Friday, July 26. This will follow (and will be held in the same
room as) the talk by Amos Ron, identified as MS57 in the Conference
Program. We hope that it will provide an opportunity for discussion of
future Group activities, especially future minisymposia. Bill Miller, our
Program Director will preside at this meeting. For those who cannot
attend the business meeting, it should be mentioned that Bill
(miller@ima.umn.edu) and Martin Muldoon (muldoon@yorku.ca), OP-SF NET
co-editor, will be attending the whole SIAM meeting and will be glad to
meet with members to discuss the Group's activities and programs.
Topic #3 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: The Editors ,
Subject: Askey and Rota Lectures during Seattle Mathfest
At the AMS-MAA Mathfest (Summer meeting) in Seattle, Washington, USA,
August 10-12, 1996, there will be four lectures dealing with binomial
coefficients and theorems:
- Gian-Carlo Rota, The many lives of binomial coefficients, August 12,
10:40 (AMS-MAA invited address)
- Richard A. Askey, The binomial theorem and some extensions
Lecture 1: Some of the history of the binomial theorem and its
extensions
Lecture 2: Refined counting and a noncommutative version of the
binomial theorem
Lecture 3: Integral analogues of the binomial theorem, orthogonal
polynomials and education
10, 11 and 12 August, 9:35. (MAA Earle Raymond Hedrick Lectures)
See "http://www.ams.org/amsmtgs/2017_other.html" for more information on
the Seattle Mathfest.
Topic #4 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: The Editors ,
Subject: Chokika (Hypergeometry) Festival in Kyushu
The following announcement appeaers on the WWW site
http://www.math.s.kobe-u.ac.jp/rchs/
September 9 (Mon) --12 (Sat), 1996
Chokika Festival in Kyushu
Department of Mathematics, Kyushu University and its neighborhood
The main purpose of this festival is to drink, eat and discuss various
subjects for our mutual understanding. Hypergeometric functions will be
served as main appetizers.
For further information, please contact:
Masaaki YOSHIDA (myoshida@math.kyushu-u.ac.jp)
Note by M.N.: Chokika is the Japanese noun which literally means
"hypergeometry". It can be used to refer to anything hypergeometric (not
only hypergeometric functions or hypergeometric equations).
Topic #5 ----------------- OP-SF NET ------------------ July 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
approximation"
* 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 on
http://www.wis.kuleuven.ac.be/wis/applied/cca.html
Topic #5 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Charles F. Dunkl
Subject: Centenary conference at Univ. of Wisconsin - Madison
University of Wisconsin to Celebrate its Mathematics PhD Centennial
On May 22-24, 1997 the Department of Mathematics of the University of
Wisconsin - Madison will celebrate the 100th anniversary of the awarding
of the first PhD in Mathematics by the University of Wisconsin in 1897.
Invited speakers, who are being asked to discuss early work at Wisconsin
and more recent work of former and current Wisconsin students and faculty,
include: Richard Arratia, Richard Askey, Carl de Boor, Robert Brown,
Joshua Chover, Michael Crandall, George Glauberman, William Jaco, Yiannis
Moschavakis, John Nohel, Louis Solomon, and Walter Rudin. In addition, we
are soliciting proposals for minisymposia organized by former students,
usually in collaboration with a current Wisconsin faculty member. There
will also be opportunities for contributed papers.
Charles Dunkl will be organizing a minisymposium there on special
functions. Mostly he will look for speakers with some important connection
to Wisconsin.
All current and former Wisconsin faculty, students, visitors, fellows, and
other `Wisconsin friends' are cordially invited to participate in the
conference. There is no registration fee. Rooms for the nights of May 21,
22, 23, and 24 (1997) have been reserved in the name of "UW-Math PhD
Centennial Conference" at three nearby hotels and will be kept open until
two weeks before the conference begins.
A banquet/celebration evening is being planned for Friday, May 23, 1997 in
Great Hall of the Memorial Union. Mary Ellen Rudin will be the banquet
speaker. Other participants will offer reminiscences. A mailing concerning
the conference to all people on the Mathematics Department's newsletter
mailing list is planned for the early fall, and this will contain further
information about registration and the banquet. Suggestions, proposals for
minisymposia, queries can be sent by email to: phdcent@math.wisc.edu or by
post to:
Richard A. Brualdi
Math Dept.
480 Lincoln Drive
UW-Madison, Madison, WI 53706, USA
These addresses can also be used to get on our mailing list.
Further information on WWW:
http://math.wisc.edu/events/cent.html
Topic #6 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Wolfram Koepf
Subject: ISAAC Congress 1997
In 1997, June 2-6, the International Society for Analysis, Applications and
Computing (ISAAC) will hold its first Congress at the University of Delaware.
Very broad area of analysis, applications and numerical analysis are
covered by the program of this Congress. The work is organized within
special sessions.
One section of this conference will be devoted to "Orthogonal Polynomials"
organized by Wolfram Keopf. The emphasis in this section will be on the
use of symbolic computation in connection with orthogonal polynomials and
special functions. Symbolic computation has the potential to change the
daily work of everybody who uses orthogonal polynomials or special
functions in research or applications. It is the purpose of the proposed
section to bring together developers of symbolic algorithms and
implementations which are connected with orthogonal polynomials and
special functions with users of computer algebra systems who need this
type of software.
Further information about the conference and the special session will
follow later.
Topic #7 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Christian Krattenthaler
Subject: 9th International Conference on Formal Power Series
and Algebraic Combinatorics, Vienna, Austria, July 14-18, 1997.
I have set up a WWW page for the conference:
http://radon.mat.univie.ac.at/People/kratt/fpsac97.html
Note from Editors: The following information was obtained from this page
on July 6, 1996:
9-th International Conference on Formal Power Series and Algebraic
Combinatorics (FPSAC'97), July 14 - 18, 1997, University of Vienna
First announcement - Call for papers
Topics: Algebraic and bijective combinatorics and their relations with
other parts of mathematics, computer science and physics.
Conference program: Invited lectures, contributed presentations, poster
session, problem session and software demonstrations.
Official languages: The official languages of the conference are English
and French.
Invited Speakers:
George Andrews (USA; not yet confirmed)
Jonathan Borwein (Canada)
Andreas Dress (Germany)
Tony Guttmann (Australia)
Mark Haiman (USA)
Michel Mendes France (France)
Rodica Simion (USA; not yet confirmed)
Anatoliy Vershik (Russia)
One more speaker to be announced.
Call for papers and posters: Authors are invited to submit extended
abstracts of at most twelve pages before November 15, 1996. Preferred way
of submission is by sending one postscript file by email to
fpsac97@risc.uni-linz.ac.at. If an author is not able to send a postscript
version of her/his extended abstract, four copies of the extended abstract
should be mailed to Peter Paule, Chairman of the Program committee of
FPSAC '97, RISC, Johannes Kepler Universitat, A-4040 Linz, AUSTRIA. The
submitted papers should begin with a summary written in the two official
languages of the conference (translations will be provided if necessary).
Authors should indicate the mode of presentation which they consider
appropriate for their paper: lecture or poster session. The notifications
of acceptance or rejection are scheduled for the beginning of March 1997.
The authors whose papers will have been accepted for a lecture or a poster
presentation will have the possibility to submit a complete version of
their work to a special issue of the journal "Discrete Mathematics,"
devoted to the conference FPSAC '97. The deadline for submission to the
special issue is September 1, 1997.
Open problem session: Contributions to the problem session are invited in
advance of the conference dates. If possible, problems should be submitted
by e-mail to the address fpsac97@risc.uni-linz.ac.at.
Software demonstrations: Demonstrations of software relevant to the topics
of the conference are encouraged. People interested in giving a software
demonstration should submit a paper as described above, including the
hardware requirements, before January 15, 1997, by email to
fpsac97@risc.uni-linz.ac.at.
Program committee: So far the list includes: Nantel Bergeron (Canada),
Peter Paule (Austria; Chairman), David Bressoud (USA), Marko Petkovsek
(Slovenia), Mireille Bousquet-Melou (France), Victor Reiner (USA), Omar
Foda (Australia), Jeff Remmel (USA), Sergey Fomin (USA, Russia),
Christophe Reutenauer (Canada), Ian Goulden (Canada), Bruno Salvy
(France), Christian Krattenthaler (Austria), Volker Strehl (Germany;
Chairman), Bernard Leclerc (France), Itaru Terada (Japan), Mark Noy
(Spain), Dominic Welsh (England).
Participant support: Limited funds are available for partial support of
participants, in particular for students and scientists from Eastern
countries. Requests should contain a letter of recommendation and include
the estimated transportation and living expenses as well as the amount of
support available from other sources. All requests should be sent in
duplicate by January 15, 1997 to the following adress : Christian
Krattenthaler, Chairman of the Organizing committee of FPSAC '97, Institut
fur Mathematik, Universitat Wien, Strudlhofgasse 4, A-1090 Vienna,
AUSTRIA.
Location: The conference will take place at the Institut fur Mathematik of
the Universitat Wien. The first talk is scheduled on July 14, 1997 at 9:00
a.m.
Hotels: To be announced later.
Further information: For any question, just write to
fpsac97@nelly.mat.univie.ac.at.
Organizing committee: Peter Kirschenhofer (Vienna), Christian Krattenthaler
(Vienna; Chairman), Daniel Krob (Paris), Helmut Prodinger (Vienna).
Registration: To be announced later.
Topic #8 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Allesandro Di Bucchianico
Subject: Report on Umbral Calculus Workshop: MIT, April 22-23, 1996}
A workshop on Umbral Calculus was held at M.I.T. on April 22--23 as an
addition to the Rotafest (the celebration of Gian-Carlo Rota's 64th
birthday). The workshop was organized by Daniel Loeb, Nigel Ray and
Alessandro Di Bucchianico with much support from Rotafest organizer
Richard Stanley and secretarial staff of M.I.T.
The goal of this workshop was to give an overview of the development since
Rota's seminal papers on the subject in the early seventies and to present
new developments. Although Umbral Calculus is classified under
combinatorics in the AMS classification, it has applications to several
fields of mathematics, including special functions. We refer to Dynamical
Survey 3 of the Electronic Journal of Combinatorics for more details.
Talks were delivered (in chronological order) by Brian Taylor, Marilena
Barnabei, Heinrich Niederhausen, Luis Verde-Star, Jet Wimp, George
Andrews, Mourad Ismail, Miguel Mendez, William Chen, Daniel Loeb, Ottavio
D'Antona, Nigel Ray, Philip Feinsilver, Henryk Gzyl, Alessandro Di
Bucchianico, and Jack Freeman. Below we will briefly summarize those talks
related to orthogonal polynomials or special functions.
- Brian Taylor presented joint work with Gian-Carlo Rota on a rigorous
foundation of the classical umbral calculus of the previous century. Brian
illustrated the high computational power of this approach by giving
one-line proofs of properties of the Bernoulli polynomials.
- Luis Verde-Star presented a very general Hopf algebra structure that
he showed to be the underlying structure of many analytic methods such as
Laplace transforms etc. As a nice application he gave a one-line
calculation without induction of the integral
\int_{0}^{\infty} x^n e^{-x} dx.
- Jet Wimp showed how cut operators on Laurent series form a powerful
tool for proving hypergeometric identities.
- Mourad Ismail discussed various properties of the Askey-Wilson
operators.
- William Chen showed how elementary identities and a clever use of the
operator \vartheta: p(x) \mapsto {p(qx)-p(x)}/x yields many basic
hypergeometric identities and transformations.
- Daniel Loeb presented ongoing joint research with Gian-Carlo Rota
and Alessandro Di Bucchianico on a basis-free infinite-dimensional umbral
calculus. As a first application, he showed how to calculate integrals of
the form \int_{||x||=1} x_1^{d_1} ... x_n^{d_n} d\mu(x), where \mu is
an orthogonally invariant measure.
- Philip Feinsilver showed results from joint research with Rene
Schott on linearization and abelianization of Lie algebras with various
applications to hypergeometric functions.
- Alessandro Di Bucchianico gave an umbral approach to variance
functions of exponential families (joint work with Daniel Loeb). He gave a
new proof of the following theorem of Philip Feinsilver: The variance
function of a natural exponential family is a polynomial of degree at most
2 if and only if the associated Sheffer polynomials are orthogonal.
- Jack Freeman showed an algebraic transform method that can be used to
find orthogonal polynomials (with respect to a linear functional) within a
certain class. He applied his method to the classes of Sheffer polynomials and
Chebyshev-like polynomials.
The workshop was attended by approximately 40 to 60 people.
Alessandro Di Bucchianico
Eindhoven University of Technology
Topic #9 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Juri M.Rappoport
Subject: Report on Chebyshev Memorial Conference
The Mechanics-Mathematics Faculty of Moscow State University, the
Chebyshev Fund and the Institute of Nuclear Power Engineering (Obninsk)
held an International Conference "Modern Problems in Mathematics and
Mechanics" - CHEB96 in honour of the great Russian mathematician Pafnutij
L'vovich Chebyshev's 175th anniversary. The conference was held in the
main high-rise building of the Moscow State University from 14th to 19th
of May 1996 and was partly sponsored by Moscow State University and the
Russian Foundation of Fundamental Investigations. The Organizing Committee
of the Conference was chaired by Academician of the Russian Academy of
Sciences, Professor N.S. Bahvalov. Among the general sections of the
conference we mention the sections on approximation theory and
computational mathematics. On Chebyshev's birthday (May 16th), a visit to
his native land, grave and museum was organized. The excursion to the
museum was very interesting because it is situated now in a country
school. A special performance devoted to mathematics and Chebyshev was
prepared by schoolboys and schoolgirls and their teachers. Among the
participants in these events were leading and famous Russian
mathematicians: the former President of the Russian Academy of Sciences,
Academician Professor G.I. Marchuk and Academician Professor S.M.
Nikolski. Some relatives of Chebyshev visited the conference also, and it
was possible to obtain their autographs. About 280 participants attended
the conference. I'd like to mention the following reports which were made
to the Conference: Academician Professor N.S. Bahvalov "The use of
Chebyshev polynomials in computational mathematics", Professor Y.
Matiasevich "Computer evaluation of generalized Chebyshev polynomials" and
the report of the author of this column: "The use of Chebyshev polynomials
in the computation of special functions".
Juri M.Rappoport
Moscow, Russian Academy of Sciences~e
Topic #10 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Charles F. Dunkl
Subject: CRM Workshop on Special Functions: CRM, May 21-26, 1996
This is a report on the Atelier sur les methodes algebriques et
q-fonctions speciales (Workshop on the Algebraic Methods and q-special
Functions), Centre de recherches mathematiques, Universite de Montreal,
Montreal, Quebec, Canada, May 21-26, 1996.
Monday, May 20, was a national holiday in Canada (Victoria Day) and this
pushed the start of the workshop to Tuesday morning. Luc Vinet,
co-organizer with Pavel Winternitz and director of the Centre, opened the
session at 9:00, welcomed the participants and dedicated the workshop to
the memory of Waleed Al-Salam, who passed away April 14 of this year (see
OP-SF NET Issue 3.3, Topic #7 for an obituary). There were approximately
seventeen invited speakers who gave hour-long talks; there were about
fourteen who contributed half-hour talks. David and Gregory Chudnovsky
were invited but were unable to attend and their time on the program was
taken by other events. Sergei Suslov was invited, could not attend, but
Dick Askey delivered his lecture. Dick also gave his own lecture (more
details later). There was indeed a heavy emphasis on q-special functions,
both of one-variable Askey-Wilson type and of several-variable Macdonald
type. The algebraic methods were highly refined and sophisticated, mostly
based on root systems and associated mathematical objects such as double
affine Hecke algebras. Here is an alphabetical list of the invited
speakers and the titles of their lectures:
- George Andrews: Plane partitions and MacMahon's partition analysis
- Richard Askey: An inequality of Vietoris and some related
hypergeometric sums
- Ivan Cherednik: Spherical difference Fourier transform
- Charles Dunkl: Intertwining operators and polynomials associated
with the symmetric group
- Pavel Etingof: Macdonald eigenvalue problem and representations of
quantum gl(n)
- Roberto Floreanini: Quantum algebras and generalized hypergeometric
functions
- Adriano Garsia: Polynomiality of the Macdonald q,t-Kostka
coefficients: a short proof
- Mourad Ismail: Moment problems and orthogonal polynomials
- Tom Koornwinder: The A_1-tableau of Dunkl-Cherednik operators
- Boris Kupershmidt: The great powers of q-calculus
- Ian Macdonald: Symmetric and non-symmetric orthogonal polynomials
- David Masson: Contiguous relations, continued fractions and
orthogonality: a ten year journey up the Askey chart
- Willard Miller, Jr.: Tensor products of q-superalgebras and
q-series identities
- Masatoshi Noumi: Raising operators for Macdonald polynomials
- Eric Opdam: Spectral analysis of Hecke algebras
- Siddhartha Sahi: Recent results on Jack polynomials and Macdonald
polynomials
- Dennis Stanton: q-orthogonal polynomials as moments
- Sergei Suslov (talk delivered by R. Askey): Some basic hypergeometric
series and q-Bessel functions.
Contributed talks were given by N. Atakishiyev, R. Chouikha, P. Floris, A.
Grunbaum, K. Kadell, M. Kapilevich, J. LeTourneux, K. Mimachi, A.
Odzijewicz, V. Spiridonov, A. Strasburger, N. Takayama, F. van Diejen, L.
Vinet. Ian Macdonald started his lecture Tuesday morning and finished it
on Wednesday. Dick Askey gave an extra half-hour talk on Wednesday
containing an overview of Askey-Wilson polynomials. Tom Koornwinder used
another one of the hours originally scheduled for the Chudnovsky's to
discuss Rene Swarttouw's web site which gives access to a vast collection
of formulas and references for the polynomials contained in the Askey
tableaux (q = 1 and general q). The URL is:
http://www.can.nl/\symbol{126}renes/index.html ; see also the software
announcement in Topic #12
There were approximately sixty participants; as well some members of the
Centre dropped in on the lectures. The languages spoken at coffee and in
the hallways appeared to be English, Russian, French, Japanese, Dutch,
Polish. The weather was mostly delightful with a few evening showers. The
University is in a scenic location near the Mont Royal; the Pavillon
Andre-Aisenstadt, which houses the Centre, is a beautifully designed and
equipped academic building, with a wonderful view of the northwest of the
city. Ian Macdonald gave the first lecture on Tuesday, Adriano Garsia gave
the last one on Saturday, thus bracketing an intense period of
leading-edge mathematics. It was generally agreed that the workshop was
excellent both in organization and inspiration to the participants for
future work. At the conclusion all applauded and thanked the organizers
for this exciting conference.
Charles Dunkl
Topic #11 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Walter Van Assche
Subject: Special Functions at the International Joint Mathematics Meeting:
Antwerp, Belgium, May 22-24, 1996
>From May 22 to 24, the American Mathematical Society and the Mathematical
Societies of the Benelux countries (Belgium, The Netherlands, and
Luxemburg) had a joint meeting in Antwerp, Belgium. The meeting was rather
successful, with about 500 people attending the conference. In the
mornings there were plenary speakers. Special sessions and contributed
papers were planned during the afternoons, with about 12 parallel sessions
each afternoon.
There was a special session on Wednesday May 22 on "Special Functions",
organized by Marcel G. de Bruin and Walter Van Assche. About 20 people
attended this special session. The first two talks were on Sobolev
orthogonal polynomials. Marcel de Bruin talked about "continuous
Sobolev-Laguerre polynomials and their generalized continued fractions". He
looked at orthogonal polynomials for the inner product
= \int_0^\infty f(x)g(x) x^\alpha e^{-x} dx
+ \lambda \int_0^\infty f'(x)g'(x) x^\alpha e^{-x} dx.
The monic orthogonal polynomials satisfy a four-term recurrence relation,
and from this Marcel de Bruin studied the corresponding generalized
continued fraction and the connection with simultaneous rational
approximation.
Henk G. Meijer then talked about "coherent pairs for Sobolev polynomials".
Coherent pairs were introduced by Iserles et al. in 1991. If (\mu_1,\mu_2)
is a coherent pair of measures, then the Sobolev orthogonal polynomials
for the inner product
= \int f(x)g(x) d\mu_1(x) + \lambda \int f'(x)g'(x) d\mu_2(x)
can be studied in detail starting from the orthogonal polynomials for the
measure \mu_1 (or the measure \mu_2). The pair (\mu,\mu), where
d\mu(x) = x^\alpha e^{-x} dx on [0,\infty), studied by de Bruin in
the previous talk, is an example of a coherent pair. Meijer recently
succeeded in finding all coherent pairs. He showed that in a coherent
pair, one of the measures needs to be classical (Jacobi, Laguerre, or
Hermite), and then the other measure is a perturbation of the classical
measure (addition of a point mass, multiplication or division by a
polynomial of degree one). Herman Bavinck then talked about "A new result
for Laguerre, Charlier, and Meixner polynomials". He showed that for all
x, \alpha \in \C
\sum_{k=j}^i k^s L_{i-k}^(-\alpha-i-1) (-x) L_{k-j}^(\alpha+j) (x) = 0,
for all i,j,s \in N, provided that i > 2s+j, and gave similar results for
Meixner polynomials and Charlier polynomials.
The next two talks were on multiple hypergeometric series. First Joris Van
Der Jeugt talked on "Transformation and summation formulas for multiple
hypergeometric functions". His starting point is the quantum theory of
angular momentum. He recalled the 3-j and the 6-j coefficients and
indicated that they are related to the Hahn polynomials and the Racah
polynomials in the Askey table. Then he looked at the 9-j coefficients,
which he considered as an inspiring source of obtaining new relations
between hypergeometric series, in particular the double hypergeometric
Kampe de Feriet series F^{0:3;3}_{1:1;1} of unit argument. Next Michael
Schlosser presented "multidimensional matrix inversions and A_r and D_r
basic hypergeometric series" (joint work with Ch. Krattenthaler). They
computed the inverse of a specific infinite r-dimensional matrix, which
they then applied to obtain many new identities for multidimensional
hypergeometric series.
Finally the remaining three talks were on computer algebra and orthogonal
polynomials. Our newsletter editor Wolfram Koepf gave two talks. The first
dealt with "efficient computation of orthogonal polynomials in computer
algebra". He mentioned various ways to compute orthogonal polynomials
(explicit series, generating functions, Rodrigues formula, differential
equation, recurrence relation, determinants) and showed how each of these
methods performs on a computer algebra system (Maple, Mathematica, Reduce,
MuPad), using the Chebyshev polynomials as a guiding example. Then he
presented "orthogonal polynomial identities in Maple V.4". Zeilberger's
algorithm gives recurrence relations and differential equations for
hypergeometric sums/integrals and is therefore quite useful for orthogonal
polynomials in the Askey table. Wolfram gave an overview of Maple's new
capabilities. This was demonstrated on the computer. Wolfram
implementations were used by Rene Swarttouw in his "computer
implementation of the Askey-Wilson scheme". Rene is presently working on a
project of creating an interactive book on orthogonal polynomials in the
Askey-Wilson scheme, with facilities for symbolic manipulation of
formulas. He first showed a clickable Askey-Wilson table, where properties
of each family of orthogonal polynomials can be found just by clicking
with the mouse on the required family. Also limit transitions can be found
by clicking the relevant arrows. Rene also worked on an interface with
Maple, allowing anyone to generate recurrence relations and differential
equations of any system of orthogonal polynomials in the Askey-Wilson
table, even after an affine transformation and rescaling. Finally he
showed that the reverse is also under construction: given the coefficients
of a three-term recurrence relation, the user will be informed with which
particular system of orthogonal polynomials one is dealing. Rene
Swarttouw's project can be seen on internet at homepage
http://star.cs.vu.nl/~rene/ . (See the next Topic - Eds.)
Walter Van Assche
Topic #12 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Rene Swarttouw and Tom Koornwinder
Topic: A computer implementation of the Askey-Wilson scheme
This is an update of the information on the project "A computer
implementation of the Askey-Wilson scheme" (see OP-SF Net 3.1, topic #16
and OP-SF Net 3.3, topic #11). During the period January - June 1996, Rene
Swarttouw has worked on this project at RIACA in Eindhoven, The
Netherlands. Tom Koornwinder was an adviser for this project. Starting
July 1, 1996 Rene Swarttouw is back at the Free University, Amsterdam, and
his main task will be in another direction. The project will be continued
in a lower gear by Swarttouw and Koornwinder until new funds have been
raised and new staff has been hired for a follow-up of the project.
To see the latest output of the project, it is best to visit
Rene Swarttouw's home page
http://star.cs.vu.nl/~rene/
and then follow the link to the Askey-Wilson scheme project. You will find
there the interactive book form of the Koekoek-Swarttouw report "The
Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue",
both in a hypertex version and in a netscape version.
You will also find there a link to CAOP, a package for calculating
formulas for orthogonal polynomials belonging to the Askey-scheme by
Maple. You can also directly approach this package at WWW:
http://www.can.nl/~demo/CAOP/CAOP.html
With the present version users can compute recurrence relations,
differential and difference equations or make a plot of every polynomial
in the Askey scheme, without having Maple installed on their own computer.
It is also possible to multiply the polynomial by a scaling function, to
change the argument and to give values to the parameters by filling out a
form, before doing the calculation. As an extra option the user can choose
the layout of the output: prettyprint, lineprint or LaTeX. The latter two
options make it possible to insert the output in another Maple worksheet
respectively in a LaTeX document by a simple mouse-action. Furthermore
there are some help pages available for users who are not familiar with
Maple. They can be viewed simultaneously while filling in the form.
Finally, Tom Koornwinder and Rene Swarttouw are writing together a
procedure in Maple, called rec2ortho, which uses the coefficients of a
three-term recurrence relation for orthogonal polynomials as input, and
which returns the explicit system of OP's solving these recurrence
relations, provided it belongs to the Askey scheme or q-Askey scheme.
Eventually, this should also be extended to associated OP's and other
explicit OP's which are not in the (q-)Askey scheme. At the moment, the
procedure only covers the OP's in the Askey scheme (q=1) up to the level
of 2 parameters (Jacobi, Meixner, etc.). For optimal usage of the
procedure you need Maple V, Release 4 (already available for Windows and
Macintosh, coming out for Sun workstation soon). The procedure rec2ortho,
as well as a test file rec2orthotest, can be obtained by anonymous ftp
from
ftp.fwi.uva.nl
cd pub/mathematics/reports/Analysis/koornwinder/rec2ortho.dir
Rene Swarttouw and Tom Koornwinder
welcome questions, comments and suggestions about this project.
Topic #13 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Editors ,
Subject: Obituary: Lawrence C. Biedenharn, Jr.
This obituary is based on material supplied by Stephen C. Milne, to
supplement a notice by Monte Basgall
(http://www.dukenews.duke.edu/Latest/Biden).
Lawrence C. Biedenharn Jr., 73, a longtime member of Duke University's
physics faculty and an internationally known researcher in theoretical
physics, died Monday, Feb. 12, in Austin, Texas, after a lengthy battle
with cancer. He had made his home in Texas in recent years.
Biedenharn became the youngest full professor on the Duke faculty -- at
age 38 -- when he was appointed in 1961. He remained at Duke until 1993,
when he retired as James B. Duke professor of physics and subsequently
moved to the University of Texas at Austin as adjunct professor. A native
of Vicksburg, Miss., he received both his bachelor's degree and his Ph.D.
from the Massachusetts Institute of Technology and served in World War II
as a Signal Corps officer and later on the staff of Gen. Douglas MacArthur
in Japan.
Serving on the faculties of Yale University and Rice University before
coming to Duke, he published six books and hundreds of research articles
in the fields of nuclear physics and later mathematical physics. He also
edited the Journal of Mathematical Physics for many years.
Biedenharn, Holman, and Louck showed how the classical work on ordinary
hypergeometric series is intimately related to the irreducible
representations of the compact group SU(2). Similarly, they found U(n)
multiple series generalizations of one-variable hypergeometric summation
and transformation theorems by comparing two ways of computing the matrix
elements of multiplicity free Wigner and Racah coefficients in U(n). This
work was done in the context of the quantum theory of angular momentum and
the special unitary groups SU(n). This work motivated the far-reaching
q-analogs that Milne, Gustafson, and their co-workers subsequently found.
Applications of this later work include unified proofs of the Macdonald
identities, constant term identities, multiple q-beta integrals, U(n+1)
and symplectic generalizations of the Bailey Transform and Bailey Lemma,
classical matrix inversion results, numerous classical summation and
transformation theorems for one-variable q-series, Rogers-Ramanujan
identities, and, finally, new infinite families of identities for sums of
squares in classical number theory.
His book about "Quantum Group Symmetry and q-tensor Algebras", jointly
written with M.A. Lohe, appeared recently; see Issue 3.2, Topic #9.
Biedenharn's work continues to motivate much of this recent research in
multivariable orthogonal polynomials, special functions, and their
applications.
Lawrence C. Biedenharn is survived by his wife of 45 years, Sarah; his son
John; daughter Sally; and two grandchildren.
Topic #14 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Richard Askey
Subject: Waleed Al-Salam
(Editors' Note: We noted the passing of Waleed Al-Salam in Issue 3.3,
Topic #7; Dick Askey has kindly provided the following additional
remarks.)
One of the pleasures in visiting Edmonton was being able to talk with
Waleed Al-Salam. The conversations could be on mathematics, but just as
frequently would be on other topics. What he did not tell me about one
visit is something which shows his character.
It was a cold winter, and he met me at the downtown airport after a flight
from Calgary. He never mentioned the sequel. I was wearing a fur hat
bought in Moscow, and carrying a bag from the International Congress of
Mathematicians in Moscow in 1966. There was a Russian hockey team in
Calgary. When this Russian looking man with a Russian hat and bag flew to
the downtown airport in Edmonton without the RCMP having been notified,
they called to Edmonton to ask that this be checked out. I did not notice
them watching, nor do I think Waleed did, but a few days later there were
questions asked about him and me at the Mathematics Department. It was
only many years later that someone else told me about this. Waleed did
not, since he did not want me to feel bad about his being investigated.
That was typical. He was a gentleman.
Waleed was also a scholar. On another trip to Edmonton, I talked about
some orthogonal polynomials which had first been found by L.J. Rogers,
although Rogers was not aware they were orthogonal. These polynomials had
been rediscovered twice around 1940, so were known to be orthogonal.
However, they were not well known. In discussion after the talk, Waleed
said that these polynomials reminded him of some polynomials found by Bill
Allaway in his thesis. Waleed had sent me this thesis, but I had not read
it carefully, so asked him to bring in a copy the next day. Sure enough,
Allaway had rediscovered these polynomials once again, but had been more
careful in his work than the two who had found these polynomials about
1940. There was a special case where division by zero ocurred unless you
were careful, and Allaway had been. These polynomials which had been
missed by others are now called sieved polynomials and they have played an
important role in a few developments of the general theory of orthogonal
polynomials. Both of Waleed's Ph.D. students, Bill Allaway and Mourad
Ismail, got a good start in mathematics from the problems which they got
from him.
I handled the paper Waleed and Ted Chihara wrote on what are now called
the Al-Salam-Chihara polynomials. This was for SIAM Journal on
Mathematical Analysis, so there should be some indication that the work
would have applications to problems in science or engineering, or some
other applied area. They had none, but the polynomials seemed so natural
that there was no question in my mind that they would eventually have many
applications. We now know where they live. They are a very important
q-extension of Laguerre and Meixner polynomials. The problem Al-Salam and
Chihara solved was a very natural extension of the problem solved by
Meixner in the middle 1930s when he found Meixner polynomials and what I
call Meixner-Pollaczek polynomials. These last arise in the
representations of SU(1,1), and so in theoretical physics. Now that
quantum groups seem to have appeared in physics, it is very likely that
these polynomials of Al-Salam and Chihara will arise in problems in
physics, just as the polynomials found earlier by Al-Salam and Carlitz
have arisen in the study of q-harmonic oscillators. These last polynomials
are natural q-extensions of Charlier polynomials. They also extend the
continuous q-Hermite polynomials of L.J. Rogers. The polynomials of Rogers
have a very interesting combinatorial structure associated with them, and
extensions of this to the Al-Salam-Carlitz polynomials is currently being
developed.
Waleed Al-Salam had a remarkable eye for formulas, and the ability and
energy to find a number of important ones. The polynomials mentioned above
are very appropriately named, and these and some other results found by
him will keep his name in the minds of many people who never had the joy
of knowing him. Those of us who did will remember him as well as his work,
and miss him the more for this.
Richard Askey
Univ. of Wisconsin-Madison
Topic #15 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Wolfram Koepf
Subject: Book Report (Feinsilver and Schott)
Algebraic Structures and Operator Calculus II:
Special Functions and Computer Science,
Mathematics and its Applications 292
By Philip Feinsilver and Rene Schott
Kluwer Academic Publishers, Dordrecht, The Netherlands,
July 1994, 160 pp., hardbound, ISBN 0-7923-2021-X,
Dfl. 120.00/ US$ 70.00
This is the second of three volumes which present, in an original way,
some of the most important tools of applied mathematics in areas such as
probability theory, operator calculus, representation theory, and special
functions, used in solving problems in mathematics, physics and computer
science.
This second volume---Special Functions and Computer Science---presents
some applications of special functions in computer science. It largely
consists of adaptations of articles that have appeared in the literature,
but here they are presented in a format made accessible for the non-expert
by providing some context. The material on group representation and Young
tableaux is introductory in nature. The algebraic approach of Chapter 2 is
original to the authors and has not appeared previously. Similarly, the
material and approach based on Appell states, so formulated, is presented
here for the first time. The solutions are tackled with the help of
various analytical techniques, such as generating functions and
probabilistic methods and insights appear regularly.
Contents:
Preface
Introduction
Basic Data Structures
Data Structures and Orthogonal Polynomials
Applications of Bessel Functions and Lommel Polynomials
Fourier Transform on Finite Groups and Related Transforms
Young Tableaux and Combinatorial Enumeration in Parallel Processing
References
Index
Wolfram Koepf
Topic #16 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Alan L. Schwartz
Subject: Call for Questions
For several years, William Connett and I have organized summer research
groups designed to give a mathematical experience to undergraduates and
high school students. A typical activity would be to use a computer
algebra system to test conjectures about orthogonal polynomials or produce
interesting graphics. We would be very grateful for any suggestions for
projects.
Topic #17 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: Angelo Melino
Subject: Problem
My research has led me to the integral
(1) int{ y*sinh(Pi*y)*K_{iy}(r)* exp(-t*y^2/2), y=0..infinity)
In words, the value of this integral is (proportional to) the inverse
Kontorovich-Lebedev transform of
f(y) := exp(-t*y^2/2).
I've searched extensively through books of Tables etc. to find a value
for this definite integral without any luck.
The original integral appeared in a paper by Marc Yor, "On some exponential
functions of Brownian Motion", Adv. Appl. Prob. 24, 509-531 (1992). It
arises in an expression for the density of the integral of a geometric
Brownian motion, conditional on its (initial and) terminal values.
Yor defines the integral (defined for r>=0 and t>0)
Theta_r(t) := r/sqrt(2*(Pi^3)*t)*exp(Pi^2/(2*t) *
int( exp(-x^2/(2*t))*sin(Pi*x/t)*exp(-r*cosh(x))*sinh(x), x=0..inf)
I can show that this integral can be expressed as
Theta_r(t) := Pi^(-2)*(the integral in (1))
I'm also able to compute the Laplace transform of this integral
Laplace (Theta_r(t)) := int( Theta_r(t)*exp(-r*p), r=0..inf)
= a/( sqrt(2*Pi*t^3)*sinh(a)) * exp(-a^2/(2*t))
where a:=cosh(p).
Topic #18 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: The Editors ,
Subject: Changes of Address, WWW pages. etc.
(1) Charles Dunkl's WWW page URL is changed to:
http://www.math.virginia.edu/~cdf5z/home.html
though there is still a link from the old location.
(2) From Paul Floris:
As from the 1st of July I have moved to Louis Pasteur University in
Strasbourg, the exact coordinates of which you find below. This change of
address is temporary and remains valid until the end of December of this
year. However, you can also still reach me at floris@wi.leidenuniv.nl.
Paul G.A. Floris
I.R.M.A.
Universite Louis Pasteur
7, rue Rene Descartes
F-67084 Strasbourg Cedex
FRANCE
floris@irma.u-strasbg.fr
(3) From Dennis Stanton
The machines names s1,s2,s3, and s7 will no longer exist at math.umn.edu.
If your e-mail aliases contain these names, mail will likely bounce.
You should change your aliases to:
name@math.umn.edu
for example,
stanton@math.umn.edu, white@math.umn.edu.
(4) New address of Rene' Swarttouw:
Vrije Universiteit Amsterdam
Fac. Mathematics and Informatics
De Boelelaan 1081
1081 HV Amsterdam
The Netherlands
Tel: +31 (0)20 4447787
E-mail: rene@cs.vu.nl
URL: http://star.cs.vu.nl/~rene
As a consequence some of the WWW addresses of the Askey-Wilson-scheme
project have moved. The best way to keep up to date is to go to Rene'
Swarttouw's Home Page and follow the links to the Askey-Wilson-scheme
project there.
(5) Walter Van Assche informs us that his WWW page URL is changed to:
http://www.wis.kuleuven.ac.be/wis/applied/walter.html
Topic #19 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: OP-SF Net editor
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 info about new submissions to a large
mailing list. Please contact him
if you want to be added to this mailing list or if your email address
on the list is no longer correct.
Since OP-SF Net 3.3 appeared, there have been no updates about new
submissions to the archive. However, the submissions directory
contains three new files which interested persons might like to download:
- kuznetsov_sklyanin... (May 7, 1996)
Separation of variables for A2 Ruijsenaars model and new integral
representation for A2 Macdonald polynomials, by V.B. Kuznetsov and
E.K. Sklyanin (31 pages, LaTex, no figures)
- elderivations11-20-95 (May 20, 1996)
Elementary derivations of summation and transformation formulas
for q-series, by George Gasper (Postscript, 16 pages)
- diejen-stokman.tex (July 1, 1996)
Multivariable $q$-Racah polynomials, 38 pages LaTeX (with AMS style
files), by Jan Felipe van Diejen and Jasper V. Stokman
Topic #20 ----------------- OP-SF NET ------------------ July 15, 1996
~~~~~~~~~
From: OP-SF Net editor
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.fwi.uva.nl, in directory
pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
or WWW:
ftp://ftp.fwi.uva.nl/pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
or WWW:
http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html
Contributions to the OP-SF Net 3.5 should reach the email
address poly@siam.org before September 1, 1996.
The Activity Group also sponsors a Newsletter edited by Wolfram Koepf.
Deadline for submissions to be included in the October 1996 issue is
September 15, 1996. Please send your Newsletter contributions directly to
the Editor:
Wolfram Koepf
Konrad-Zuse-Zentrum
Heilbronner Str. 10,
D-10711 Berlin, Germany
tel.: +49-30-896 04-216
fax: +49-30-896 04-125,
email: koepf@zib-berlin.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
otherwise.
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:
http://www.zib-berlin.de/~bzfkoepf/
or by anonymous ftp at
ftp.zib-berlin.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 .
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