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July 15, 2000
O P - S F N E T Volume 7, Number 4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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. From the Editor
2. Conference on q-series
3. Second Announcement of the SIDE IV Meeting
4. Workshop on Quasiclassical and Quantum Structures
5. 2001: A Mathematics Odyssey
6. Dortmund meeting on Approximation Theory
7. Reports on Special Functions 2000
8. Future Directions in Special Functions
9. 8th International Krawtchouk Conference
10. Jose J. Guadalupe (1946-2000)
11. Authors Selected for NIST Digital Library Project
12. Special Functions Posters
13. OP-SF preprints in xxx archive
14. Changes of address, WWW pages, etc.
15. About the Activity Group
16. Submitting contributions to OP-SF NET and Newsletter
Calendar of Events:
2000
July 19-26: Third World Congress of Nonlinear Analysts,
Catania, Italy (including session on
"Adaptive quadrature and cubature formulae". 7.1 #6
July 24-28: Summer School "Orthogonal Polynomials and Special
Functions", Laredo, Spain. 6.6 #3
Dedicated to Jose Javier Guadalupe
August 5-8: International Symposium on Analysis, Combinatorics
and Computing, Dalian, China 7.1 #7
August 14-18: International Symposium on Applied Mathematics,
Dalian, China 6.5 #5
September 22-28: International Conference on Functional Analysis
and Approximation Theory, Acquafredda di
Maratea, Italy 7.2 #6
October 26-28: q-Series with Applications to Combinatorics,
Number Theory and Physics, University of
Illinois, USA 7.4 #2
November 27 - December 1: 4th International Interdisciplinary
meeting on "Symmetries and Integrability of
Difference Equations", Tokyo, Japan. 7.4 #3
2001
January 9-14: Workshop on Quasiclassical and Quantum Structures,
Fields Institute, Toronto, Canada 7.4 #4
June 18-22: Symposium on Orthogonal Polynomials, Special Functions and
Applications, Rome, Italy 7.3 #2
August 6-10: Analytic theory of continued fractions, orthogonal
functions and related topics, Grand Junction,
Colorado, USA 7.4 #5
August 20-24: 3rd International meeting on Approximation
Theory, Dortmund, Germany 7.4 #6
October 1-5: "Numerical Algorithms", Conference in Honor of Claude
Brezinski, Marrakesh, Morocco 7.3 #3
Future plans:
As already mentioned in OP-SF NET 6.5, the next meeting in the series
Fields-Toronto (1995) - CRM-Montreal (1996) - Mount Holyoke (1998) - Hong
Kong (1999) - Arizona (2000) is expected to be held in Amsterdam, in
2002, probably in early summer, to be organized by Tom Koornwinder
(thk@uwa.wins.nl), Nico Temme (nico@cwi.nl) and Erik Koelink
(koelink@twi.tudelft.nl).
Topic #1 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: From the Editor
Since the appearance of our last issue the major NATO ASI and Conference
has taken place in Tempe, Arizona. In this issue, we feature reports from
some of those attending (Erik Koelink, Kathy Driver and Bill Connett)
(Topic #7) as well as a detailed report on the session on "Future
Directions" by Walter Van Assche (Topic #8).
After some discussion between the Officers of the Activity Group, I
decided to reduce the information in "OP-SF preprints in xxx archive" to
simply giving abstract numbers, authors, titles and e-mail addresses. We
continue to discuss how much detail to include in conference
announcements. It has been suggested that it would be sufficient to
include titles, location and dates with a link to the conference web page.
On the other hand, there seems to be a number of readers for whom web
access is not yet fast and efficient so that there remains a need for more
information on conferences in OP-SF NET.
I continue to ask for a volunteer or volunteers to take over as Editor
from January 1, 2001.
Topic #2 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Conference on q-series
The following is a selection of the information on the web site:
http://www.math.wisc.edu/~ono/qseries.html
q-series with Applications to Combinatorics,
Number Theory and Physics.
October 26-28, 2000
University of Illinois at Urbana-Champaign.
Confirmed Plenary Speakers
Scott Ahlgren (Colgate University)
George Andrews (Penn State University)
Richard Askey (University of Wisconsin)
Anne Schilling (MIT)
Dennis Stanton (University of Minnesota)
Confirmed Invited Speakers
Krishnaswami Alladi (University of Florida)
Douglas Bowman (University of Illinois)
Thomas Ernst (Uppsala University)
Mourad Ismail (University of South Florida)
Christian Krattenthaler (University of Vienna)
Jeremy Lovejoy (University of Wisconsin)
John McKay (Concordia University)
Steve Milne (Ohio State University)
Katsuhisa Mimachi (Kyushu University)
Morris Newman (University of California,
Santa Barbara)
Peter Paule (University of Linz)-tentative
Sasha Polishchuk (Boston University)
Mizan Rahman (Carleton University)
Ole Warnaar (University of Amsterdam) - tentative
Sander Zwegers (University of Utrecht)
Registration:
Registration information will be available soon.
To be placed an an e-mail list, send an e-mail to
berndt@math.uiuc.edu
Financial support is available to a limited number of
participants with some preference given to graduate
students and new PhD's. To apply for this support,
send e-mail to ono@math.wisc.edu by September
1, 2000.
Scientific Organizer
Bruce Berndt and Ken Ono
Topic #3 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: Tetsuji Tokihiro
Subject: Second Announcement of the SIDE IV Meeting
4th International Interdisciplinary Meeting on
"Symmetries and Integrability of Difference Equations"
Tokyo (Japan), 27 November - 1 December 2000
The SIDE meetings are intended to provide a point of contact between
researchers of various disciplines, all working or using methods from
discrete systems, i.e. systems that can be described by ordinary or
partial difference equations.
This domain forms the core of a great variety of fields, including
classical and quantum physics, computer science, mathematical biology,
economics, numerical analysis, discrete geometry, and so on.
The main topics of the present meeting will be:
Integrable difference equations, symmetries of ordinary and partial difference
equations, cellular automata, discrete monodromy problems, q-special functions,
discrete geometry, applications to physics and engineering.
In this meeting, lectures will be delivered in the auditorium of the
Graduate School of Mathematical Sciences, University of Tokyo.
(Information is available on http://liaison.ms.u-tokyo.ac.jp/)
Since our idea is to keep to a single session format, we plan to accept
only a restricted number of applications. All of the talks will be from 20
to 30 minutes long. We will also organize poster sessions.
The cost of participation consists of a registration fee (including
excursion and banquet) of 15,000 Japanese-yen.
As for the accommodation, we are happy to provide reservations in the hotel:
HILPORT HOTEL
Sakuraoka-cho 23-19, Shibuya-ku, Tokyo 150-0031, Japan
Tel. (+81)3-3462-5171
Fax. (+81)3-3496-2066
at the price of 12,000 Japanese yen (all inclusive, i.e. breakfast, lunch and
dinner) or 9,500 Japanese yen (with breakfast only) per day.
The following list is the expected participants at present:
Mark ABLOWITZ (Colorado University, USA)
Vsevolod ADLER (Ufa Institute of Mathematics, Russia)
Claude BREZINSKI (Universite' des Sciences et Technologies de Lille, France)
Robert CONTE (CEA--Saclay, France)
Adam DOLIWA (Warsaw University, Poland)
Claire GILSON (University of Glasgow, UK)
Basile GRAMMATICOS (Universite' Paris VII, France)
Valeri GROMAK (Belarus State University, Belarus)
Jarmo HIETARINTA (University of Turku, Finland)
Ryogo HIROTA (Waseda University, Japan)
Xing-Biao HU (Academia Sinica, China)
Mourad ISMAIL (University of South Florida, USA)
Michio JIMBO (University of Tokyo, Japan)
Nalini JOSHI (University of Adelaide, Australia)
Kenji KAJIWARA (Doshisha University, Japan)
Rinat KASHAEV (Steklov Math. Institute, Russia)
Boris KONOPELCHENKO (Universita di Lecce, Italy)
Martin KRUSKAL (University of Rutgers, USA)
Franklin LAMBERT (Vrije Universiteit Brussel, Belgium)
Decio LEVI (Universita' di Roma Tre, Italy)
Sergey LEBLE (Technical University of Gda\'nsk, Poland )
Yoshimasa NAKAMURA (Osaka University, Japan)
Atsushi NAGAI (Osaka University, Japan)
Frank NIJHOFF (University of Leeds, UK)
Jon NIMMO (University of Glasgow, UK)
Katsuhiro NISHINARI (Ryukoku University, Japan)
Masatoshi NOUMI (Kobe University, Japan)
Yasuhiro OHTA (Hiroshima University, Japan)
Kazuo OKAMOTO (University of Tokyo, Japan)
Reinout QUISPEL (Latrobe University, Australia)
Orlando RAGNISCO (University of Roma, Italy)
Alfred RAMANI (Ecole Polytechnique, France)
Jean-Pierre RAMIS (Universite' Toulouse, France)
Simon RUIJSENAARS (CRM, Netherlands)
Hidetaka SAKAI (University of Tokyo, Japan)
Paolo SANTINI (University of Roma, Italy)
Wolfgang SCHIEF (University of New South Wales, Australia)
Serguei SERGUEEV (BLTP JINR, Russia)
Evgueni SKLYANIN (Steklov Institute of Mathematics at St. Petersburg, Russia)
Juri SURIS (Technische Universitaet Berlin, Germany)
Daisuke TAKAHASHI (Waseda University, Japan)
Munirathinam TAMIZHMANI (Pondicherry University, India)
Morikazu TODA (Honorary Chairperson)
Walter VAN ASSCHE (Katholieke Universiteit Leuven, Belgium)
Ralph WILLOX (University of Tokyo, Japan & Vrije Universiteit Brussel, Belgium)
Pavel WINTERNITZ (Universite de Montreal, Canada)
Youjin ZHANG (Tsinghua University, China)
If you are interested in attending, please visit the web site:
http://elrond.doshisha.ac.jp/side4/index.html
where you can find the application form which should be sent to us.
Information updates will be available on this web site.
Alternatively, you can get an application form from the organizers.
Postal address:
SIDE IV
Graduate School of Mathematical Sciences
University of Tokyo
3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, JAPAN
Fax: (+81) 3-5465-8312
email: side4-org@elrond.doshisha.ac.jp
website: http://elrond.doshisha.ac.jp/side4/index.html
email: side4-org@elrond.doshisha.ac.jp
Local organizers are:
J. Satsuma, T. Tokihiro
(Graduate School of Mathematical Sciences, University of Tokyo,
3-8-1 Komaba, Meguro-ku, Tokyo153-8914, Japan)
e-mail: satsuma@poisson.ms.u-tokyo.ac.jp
toki@poisson.ms.u-tokyo.ac.jp
fax: +81-3-5465-8312
Topic #4 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Workshop on Quasiclassical and Quantum Structures
>From http://www.fields.utoronto.ca/lt-qq.html
Workshop on
Quasiclassical and Quantum
Structures
Tuesday, January 9 - Sunday, January 14, 2001
at the Fields Institute
Toronto, Ontario, Canada
Organizers:
Pavel Etingof, Massachusetts Institute of Technology
Boris Khesin, University of Toronto
Topics include:
- Classical and quantum integrable systems
- Macdonald theory
- Poisson-Lie groups, quantum groups, dynamical quantum groups, and
quantization
- Infinite-dimensional Lie algebras and structures, and their quantum
deformations
- q-Virasoro, q-W-algebras and their quasiclassical limits, affine and quantum
affine algebras at the critical level
- Quantization of Poisson manifolds
- Hypergeometric and q-hypergeometric functions, their generalizations, KZ,
qKZ, KZB, qKZB equations, Elliptic quantum groups
Limited funds may be available to assist graduate students and postdoctoral
participants.
Please contact the organizers by fax at: (416) 348-9759, or through
e-mail at:
lt-structure@fields.utoronto.ca.
All are welcome.
This Workshop is part of the "Infinite-dimensional Lie Theory and its
Applications" and "Symplectic Geometry, Topology, and Gauge Theory"
programs, both hosted by the Fields Institute in Fall 2000 and Spring
2001, respectively.
Contact mailing address:
c/o Lie Theory, The Fields Institute
222 College Street, Toronto, Ontario M5T 3J1
Telephone: (416) 348-9710
Fax: (416) 348-9759
Topic #5 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: Phil Gustafson
Subject: 2001: A Mathematics Odyssey
FIRST ANNOUNCEMENT
2001: A Mathematics Odyssey
a conference on
the analytic theory of continued fractions,
orthogonal functions, rational approximation
and related topics.
A Celebration of the 70th birthday of
Dr. William B. Jones
Professor Emeritus, University of Colorado, Boulder, USA
In recognition of the contributions Professor William B. Jones has made to
the field of continued fractions and rational approximation, we are
pleased to announce a conference organized in his honor. The conference
will be held August 6-10, 2001, at Mesa State College in Grand Junction,
Colorado, USA. We invite contributions from both the theoretical and
computational aspects of continued fractions, orthogonal polynomials,
rational approximation, and related areas and applications.
There is no need to commit to attending the conference at this time.
However, if you are interested in receiving a second announcement and
would like to be on our mailing list, please respond or email to one of
the organizers at the address below, including your name, mailing address
and email address.
More information about Mesa State College and Grand Junction,
Colorado, can be found at http://www.mesastate.edu, and
http://www2.mesastate.edu/community_links.htm.
We hope to see you there.
Organizers:
Cathy Bonan-Hamada, Phil Gustafson
Mathematics Department
Mesa State College
1100 North Ave.
Grand Junction, CO 81501-3122 USA
cbonan@mesastate.edu, pgustafs@mesastate.edu
Topic #6 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: IDoMAT 2001 - Dortmund meeting on Approximation Theory
From:
http://www.mathematik.uni-dortmund.de/lsviii/idomat2001.html
3rd INTERNATIONAL DORTMUND MEETING
APPROXIMATION THEORY
IDoMAT 2001
August 20 - 24, 2001
Haus Bommerholz - Witten, Germany.
Organizers:
Martin D. Buhmann, University of Giessen
martin.buhmann@math.uni-giessen.de
Detlef H. Mache, University of Dortmund,
mache@math.uni-dortmund.de
Manfred W. Müller, University of Dortmund.
mueller@math.uni-dortmund.de
The main aim of this conference IDoMAT 2001 is to bring together invited
researcher, to discuss problems and to promote the transfer of results,
ideas and applicable methods in the following fields in the Theory of
Constructive Approximation:
Approximation Methods, Approximation by Operators, Interpolation
Radial Basis Functions
Orthogonal Polynomials
(Multi-) Wavelets, Neuronal Networks, CAGD
Proceedings of IDoMAT 2001 and accepted research papers:
We intend to publish the invited lectures and the accepted research papers
in the Proceedings (Volume 3): New Topics in Constructive Approximation.
This third Volume (after Volume 1: Approximation Theory - IDoMAT 95
(Akademie Verlag Berlin) and Volume 2: New Developments in Approximation
Theory - IDoMAT 98 (Birkhäuser Verlag Basel)) will be published in the
International Series of Numerical Mathematics by Birkhäuser Verlag Basel.
IDoMAT 2001 - Office: University of Dortmund
Institute of Applied Mathematics (Approximation Theory, LS VIII)
D - 44221 Dortmund (Germany)
E-mail: idomat@math.uni-dortmund.de
Topic #7 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Reports on Special Functions 2000
Special Functions 2000: Current Perspective and Future Directions,
Arizona State University, May 29 to June 9, 2000.
1. From Erik Koelink
The 2-week conference actually consisted of three parts. A NATO Advanced
Study Institute, a NSF Research Conference and a series of lectures on
Computer Algebra. The NATO ASI talks were plenary 1-hour talks on various
subjects. These talks ranged from introductory talks to more advanced
talks on recent results. To mention a few, I very much liked the talks by
Christian Krattenthaler (a great performer with transparencies and
figures), Mizan Rahman (associated orthogonal polynomials and Askey-Wilson
operators), Simon Ruijsenaars (solutions of the Askey-Wilson difference
operators with q on the unit circle), Percy Deift (Riemann-Hilbert
problems, and their application to all kinds of problems), Ken Ono (recent
exiting results in number theory), Slava Spiridonov (a very impressive
account of factorisations and their use), Sergei Suslov (q-Fourier series
and a q-Riemann zeta function), Alexei Zhedanov (biorthogonal rational
functions), Hjalmar Rosengren (dynamical Yang-Baxter equation and n-j
symbols, n=3,6,9). The above list consists more of the talks on more
recent results, and there were also some very good introductions by Dennis
Stanton and Mourad Ismail. Maybe I should mention all speakers in this
programme, since the talks were in general very good and very interesting.
The half-hour talks in the NSF-programme were organised in parallel
sessions, so that it's impossible to attend them all. Some of my personal
favourites were Jan Felipe van Diejen on a multivariable summation formula
for elliptic hypergeometric series conjectured by Ole Warnaar that he
could almost prove, Katsuhisa Mimachi on representations of the Hecke
algebra on twisted homology, Andre Unterberger on relativistic
quantisation applied to special functions, Michitomo Nishizawa on all
kinds of generalisations of the gamma function and Joaquin Bustoz on
q-Bessel functions and q-Lommel polynomials.
The talks in the Computer Algebra part were usually scheduled in the
evening, which is one of the reasons that I missed a number of them. Some
of these talks were presentations by people from Mathematica who discussed
their huge posters on special functions.
The chief of the (local) organisation was Sergei Suslov and he has made a
tremendous effort in making the conference such a success. His daughter
Liliya has been a great help in organising. All in all the organising
committee has done a very nice job. The Tempe surroundings were very
pleasant, but also very hot. The Grand Canyon was one of the touristic
events and, being an inhabitant of a flat country, I was really impressed
with it.
2. From Kathy Driver <036KAD@cosmos.wits.ac.za>
Over 100 mathematicians gathered in Tempe to discuss Current Perspectives
and Future Directions in the area of Special Functions. The meeting was
remarkable from several different perspectives, perhaps the most striking
feature being the diversity of areas in which talks were presented. The
old maxim that "special functions are everywhere" gained considerable
credibility as a variety of topics unfolded both in the main presentations
and also during the parallel sessions. Orthogonal polynomials , special
functions of one and several variables, asymptotics, continued fractions,
applications to number theory, combinatorics and mathematical physics,
integrable systems, harmonic analysis and quantum groups, Painleve
classification were listed as some of the topics to be covered and that
was no exaggeration--these and many others featured in a lively and well-
organised programme.
Many of the well-established masters in the area presented talks, mostly
for two separate hours which facilitated more than just a glimpse of their
ideas and expertise and attendance by graduate students was noteworthy.
Richard Askey commented in his speech at the banquet that he was grateful
to those present for carrying the banner of special functions forward over
the past ten years and it was easy to see why he is pleased with
developments in the field.
The venue was comfortable and suitable, the organisational details were taken
care of in exemplary fashion and the power failure was thankfully short in
duration, given the formidable heat in the desert at that time of year.
attended. This was an extremely successful meeting and bodes very well for
continuing vigorous interest in this area.
3. From William Connett
It was hot. The sun was a terrifying presence. Your reporter would
look out the window of the conference center and he could see for two
miles down Apache Boulevard, and often not a single person could be seen
in the open in this very modern city. Although the temperature of the air
was over 100 F, nobody went into the swimming pool during the day because
the temperature of the pool was above 90 F and the sun was so intense that
it would give you skin cancer in five minutes. On the other hand it was
not the hottest mathematical meeting that your reporter ever attended. I
remember one epic meeting in Morocco in July when there was no air
conditioning in the hotel, no water in the rest rooms, the temperature one
day got up to 130F, and all the lectures were in French.
By that standard, this meeting was a cake walk. The Holiday Inn was
a very pleasant venue. There was so much air conditioning in the
conference hall that most participants wore their jackets, the food was
serviceable and easy to obtain, and the lay out of the conference with all
lectures, food, and rooms in one location made it a very pleasant meeting.
The weather kept all the participants in the motel, so that mathematical
conversations were spontaneous and quite easy.
This was one of the most complex meetings that I have ever attended.
It was concurrently: first, a NATO funded Advanced Study Institute,
second, a NSF funded Research Conference, and third, a mini conference on
Computer Algebra and Special Functions on the Web, supported by Wolfram
Research and other sources. This may become the new paradigm for
organizing a conference. The field of special functions has grown so
enormously that it is difficult to remember the time when the few
enthusiasts could easily fit into a small seminar room to discuss the
problems of common interest. Now there is a cast of hundreds, working in
dozens of areas. The specialty meeting now take on more of the character
of the large national meetings.
And the total experience was quite enjoyable. The NATO funded
Advanced Study Institute featured a number of hour long talks which were
intended to introduce a topic, and bring a sophisticated audience up to a
certain level of competence on a particular problem. For example, Luc
Vinet gave two lectures entitled "Advances in multivariable special
functions and mathematical physics", but actually he had the courage to
ignore the physics, and work through several concrete examples of the new
families of symmetric polynomials called atoms, related to the t-Kostka
polynomials. The examples were carefully done, and the audience was very
appreciative of the care with which they were explained. Two other
speakers in this section that I really enjoyed were Christian
Krattenthaler who gave a lovely series of lectures on plane partitions,
orthogonal polynomials, and hypergeometric series. Christian certainly
wins the prize for the most innovative use of the overhead projector in
his presentations. Even if I did not enjoy the topic, I would be
fascinated by his implementation of ur-animation in his talks. His screen
reminds me of some of the early Loony Toons cartoons with the jerky but
eye-catching animation. The other speaker was Alexander Kitaev, who
introduced the audience to the six versions of the Painleve equation and
their solutions. I was very appreciative of his effort to explain to the
outsider what was going on in this important area.
The NSF research Conference included many more traditional research
type talks, from this feast of topics, I will mention two that I found
particularly memorable: Yuan Xu talked about problems in Fourier
expansions in several variables, and Khalifa Trimeche worked out the
harmonic analysis associated with a singular differential-difference
operator (a generalization of the Dunkl operator on the real line).
There were many other excellent talks.
The final part of the conference were the sessions on computer
algebra. real indication of the interest in these topics (or perhaps just
the weather) that even though the meetings started at 8:00am and went all
day with only an hour for lunch and dinner, there would frequently be over
one hundred people in the lecture hall at 9:00pm to hear Oleg Marichev or
Michael Trott from Mathematica talk about their product, or Lance
Littlejohn or Axel Riese talk about some new software that they had
produced to simplify certain calculations. The wealth of computational
tools now available is truly impressive.
Many talks were given in many areas, and this brief note can only
mention a few of them. On the other hand, I think it is important to try
and see what the new tools or new areas where great progress is being
made. I will mention three. First, it is quite clear from the talks of
Dunkl, Xu, Littlejohn, Kill, Haine and others that finally a theory of
multivariable polynomials is beginning to emerge. We may not agree on
which of these polynomials to call classical, but we are beginning to see
the clear lines of the theory. I look forward to the new book from Dunkl
and Xu. Second, it was clear from the talks of Percy Deift and Walter Van
Assche that the techniques developed to solve the Riemann-Hilbert problem
are providing powerful new tools for the study of orthogonal polynomials.
Finally, I have gone to many meeting and never heard mentioned the
solutions of the Painleve equation. Such solutions were not on everyone's
lips at this meeting, but they were mentioned in at least five different
talks, and they were the subject of two hours of plenary talks. We will
hear much more about "the Painleve Transcendents".
Finally we must thank the organizing committee: Bustoz, Ismail,
Koornwinder, Spiridonov, Suslov, and Vinet for a splendid program, and the
gracious hosts from Arizona State University, Sergi Suslov and Joaquin
Bustoz for a wonderful scientific adventure in a very hot corner of the
world. Hot mathematics in a hot place!
Topic #8 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: Walter Van Assche
Subject: Future Directions in Special Functions
[From the June Newsletter]
On the last day of the NATO Advanced Study Institute on "Special functions
2000: Present Perspectives and Future Directions" (Tempe, Arizona, May 29
- June 9, 2000) there was a session on Future Directions, chaired by
Richard Askey. The following is an attempt to summarize what was said.
First Askey gave some _advice_.
- Ramanujan is still a very big source of future research, especially
regarding congruences for the partition function. Exciting new results
have been found by Ken Ono, but what has been found is probably only a
hint of what else will be discovered.
- Other indications that there is still a lot to be learned from a study
of Ramanujan is the recent work on elliptic functions with different
bases, which was probably the first use of cubic transformations of
hypergeometric functions, Ramanujan's wonderful series for 1/\pi and the
remarkable identities found in the lost notebook (including results on
mock theta functions).
- A second source of problems is in the work of David and Gregory
Chudnovsky. They have mentioned many problems and results, some of which
are eventually published, but many have not been published. Their papers
are worth studying, although this is not easy.
- Work of Rodney Baxter led to the discovery of quantum groups and was one
of the sources for elliptic hypergeometric functions. There is much more
there which needs to be understood.
- Bill Gosper has sent e-mail containing many interesting formulas to many
people. Some e-mails have been understood, but many still are full of
mysteries.
He then continued with some _safe_predictions_:
- Special functions of several variables will be studied extensively
(orthogonal polynomials, hypergeometric and basic hypergeometric
functions, elliptic hypergeometric functions).
- Cubic transformations will get more attention (see, e.g., Bressoud's
treatment of alternating sign matrices).
- There will be much more combinatorial work.
- Computer algebra will become important but will not replace thinking.
- Nonlinear equations and special functions (Painleve) will receive more
attention.
- Regarding asymptotics, there will be a deeper understanding in one variable,
there will be much more on difference equations, and asymptotics for several
variables will be developed more fully.
Askey then expressed some _hopes_:
- Special functions in infinite dimensional spaces will appear.
- Linear differential equations with more than three regular singular points
will be understood better than at present.
- Special functions over p-adic and finite fields become more popular.
- Orthogonal (and biorthogonal) rational functions will start to have more
applications.
- Understanding mock theta functions via mock modular functions will partly
succeed.
- The location of zeros of _2F_1(a,b;c;z) on (-\infty,0), (0,1), and
(1,\infty) in the terminating case is known (also in the complex plane).
We need extensions to _3F_2 and _2\phi_1 and other (basic) hypergeometric
functions.
Finally Askey mentioned some _wild_guesses_:
- Cubic transformations for hypergeometric functions really live in double
series associated to G_2 and we are only seeing one dimensional parts of
this.
- The function G satisfying the relation G(x+1) = \Gamma(x) G(x) has an
integral representation, probably an infinite dimensional one (a limit of
Selberg's integral?).
- 9-j symbols as orthogonal polynomials in two variables can be
represented as a double series.
Some other participants added some other interesting observations
and suggestions for future work.
Tom Koornwinder:
- Matrix valued special functions. An obvious source of such functions are
the generalized spherical functions associated with Riemannian symmetric
pairs (G,K) and higher dimensional representations of K. See Grunbaum's
lecture at this meeting for the example (SU(3),SU(2)).
- Orthogonal polynomials depending on non-commuting variables naturally
occur in connection with quantum groups, see for instance the q-disk
polynomials studied by Paul Floris, which are spherical functions for the
quantum Gelfand pair (U_q(n), U_q(n-1)). More examples should be obtained
and a general theory of such polynomials should be set up.
- Special functions associated with affine Lie algebras. Remarkable
interpretations of special functions have already been found on affine Lie
algebras (see the book by Victor Kac), but much more should be possible
here. The lecture by Paul Terwilliger at this meeting gives some hints in
this direction.
- The work of Borcherds: generalized Kac-Moody algebras, vertex algebras and
lattices in relationship with automorphic functions.
- Algebraic and combinatorial techniques in contrast with analytic
techniques have quickly gained importance in work on (q-)special functions
during the last few decades. Algebra often gives rise to quick and easy
formal proofs of, for instance, limit results. Usually, a rigorous
analytic proof is much longer, while it does not give new insights. In
fact, the rigorous proof is often omitted. There is need for a meta-theory
which explains why formally obtained results are so often correct results.
Vyacheslav Spiridonov:
- It is likely that important special functions are hidden in some of the
work on differential-delay and differential-difference equations.
- Development of elliptic special functions (elliptic beta integral, elliptic
deformations of Painleve).
- Connections of our work with other fields (biology, economy, etc.).
- Wavelets could be studied as special functions.
- Ismail's q-discriminant needs an interpretation in statistical mechanics.
Stephen Milne and Tom Koornwinder:
- The lecture by Jan Felipe van Diejen and the discussion after Stephen
Milne's last lecture at this meeting made clear that several different
types of multivariable analogues of one-variable (q-)hypergeometric series
have been studied extensively, but that their mutual relationship is
poorly understood. The three most important types are:
1. Explicit series associated to classical root systems
(Biedenharn, Gustafson, Milne),
2. Hecke-Opdam hypergeometric functions and Macdonald polynomials
associated to any root system ((q-)differential equations, usually no
explicit series),
3. Gelfand hypergeometric functions (again (q-)differential equations,
usually no explicit series).
Van Diejen, in his lecture, added to this list:
4. hypergeometric sums of q-Selberg type,
5. hypergeometric sums coming from matrix inversion.
Koornwinder would like to add:
6. Solutions of KZ(B) and q-KZ(B) equations,
7. 3-j, 6-j and 9-j symbols for higher rank groups.
- Elliptic generalizations of one and multivariable hypergeometric
functions are also coming up now. Stephen Milne added that it is likely
that the concept "very well poised" ties these various types of
multivariable functions together.
- Applications in combinatorics and number theory are welcome.
Sergei Suslov:
- One needs to understand the classical q-functions, beginning with the
q-exponential and q-trigonometric functions.
- Orthogonal q-functions (also the non-terminating series) and
special limiting cases are useful.
- Biorthogonal rational functions are a rich source of research problems.
Mourad Ismail:
- There is still a lot of work to be done in moment problems and continued
fractions, in particular indeterminate moment problems.
- Discriminants, lowering operators and electrostatics, such as the Coulomb
gas model.
- Multivariate extensions.
Walter Van Assche: There is still quite some work in orthogonal polynomials:
- The asymptotic zero distribution and logarithmic potential theory (with
external fields and constraints) has been worked out in quite some detail now.
For some q-polynomials one seems to need circular symmetric weights. We don't
know how to handle big q-Jacobi, big q-Laguerre, q-Hahn and q-Racah yet.
- There is a well established theory for strong asymptotics of orthogonal
polynomials on the unit circle and on the interval [-1,1] (Szego's
theory). The analog of this theory for the infinite interval (e.g., Freud
weights) is starting to become clear. So far there is no theory for
orthogonal polynomials on a discrete set (such as the integers). The
Riemann-Hilbert technique may be useful here.
- Multivariate orthogonal polynomials need more attention.
- Multiple orthogonal polynomials (one variable but several weights) may
be a rich source of nice research. Some of these multiple orthogonal
polynomials can be written in terms of nice special functions (generalized
hypergeometric functions, hypergeometric functions of several variables,
etc.). The analysis involves Riemann surfaces with several sheets,
equilibrium problems for vector potentials, banded non-symmetric
operators. We already know some nice applications in number theory and
dynamical systems. Other applications would be nice.
- Higher order recurrence relations and asymptotics for solutions of
difference equations are useful.
George Gasper:
Positivity proofs and proofs that certain functions only have real zeros
are very useful.
Erik Koelink
- The _8\phi_7 basic hypergeometric is very nice and the multivariate
case would be even nicer.
- Where do the elliptic hypergeometric functions of Frenkel and Turaev live?
- Is there a way to use Riemann-Hilbert problems for quantum groups?
- Applications of multivariate orthogonal polynomials in probability theory.
This is just a brief description and a personal account of what was said
during the session on future directions. Some other participants added
some open problems, but it would take too much space to report on these in
the newsletter.
Topic #9 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: Vadim Zelenkov
Subject: 8th International Krawtchouk Conference
The Eighth International Krawtchouk Conference was held in the period May
11-14, 2000. The conference was organized by the Institute of Mathematics
(National Academy of Sciences of the Ukraine), the Kiev National
Shevchenko University, the National Drahomanov Pedagogical University and
the National Technical University of the Ukraine (KPI). It took place in
Kiev (Kyiv), the capital of the Ukraine.
The 626 participants represented Algeria, Armenia, Australia, Belarus, Italy,
Kazakhstan, Lithuania, Russia, Ukraine and USA. Following tradition, the
Conference included four sections:
- Differential and integral equations, and applications
- Algebra, geometry. Mathematical and numerical analysis
- Theory of probability and mathematical statistics
- History, methods of teaching of mathematics
The titles of the reports which are most relevant to orthogonal
polynomials and special functions (organized "by functions") are:
Savva V.A., Khlus O.V.: Krawtchouk Quantum Oscillator: Dynamics Features
Groza V.A.: The Quantum Group SU_q(2) and Product Formula for q-Krawtchouk
Polynomials
Zelenkov V.I.: Orthogonal Polynomials Given by Recurrence Relation
Mamteev J.A., Huchraeva T.S., Burjacov A.N.: The Solution of a Contact Problem
Using the Modified Struve and Bessel Functions
Ivcina A.E., Huchraeva T.S., Stukalina V.I.: On Modified Struve Function
and the Principal Characteristic
Mamteev J.A., Stukalina V.I.: Modified Struve Function L_\nu(z) and Struve
Function H_\nu(z)
Markova K.V.: Inversion Formula for Hankel Transform for a Class of Functions
Gaidey V.O.: On Generalization of Bessel Function
Bilyk Yu.: On Multiplication Theorem for Generalized Hypergeometric Functions
Warren D., Seneta E.: Hypergeometric Polynomial Probability Generating
Functions
Nikitina O.M.: Finite Hybrid Integral Transforms of Mehler-Fock Type of
the First Kind
Romanenko N.V.: Fourier Series with Mathieu Functions
Timan M.F.: On Fourier Series with Monotonic Coefficients
Tretyakova N.N.: Limit Relations Between Some Integral Transforms
Yakubovich S.B.: On the Titchmarsh Integral Transformation
The book of abstracts contains 560 pages.
As in the previous conferences the opening ceremony was dedicated to the
memory of M. Krawtchouk. A memorial booklet "Son of the Sky" was presented
by Galina Datsyuk and Mikola Soroka.
The second book published on the eve of the conference is the collection
of Krawtchouk's popular scientific works. It includes in particular
studies in the history of mathematics (e.g. Euler's Influence on the
further Development of Mathematics), popular physical articles (Space,
Time, Matter) scientific reports and lyrical notes about the author's
travel to the World Mathematical Congress in Bologna and others. The book
also contains the biography of M. Krawtchouk written by Prof. Nina
Virchenko who has provide and inspired investigations of Krawtchouk's life
and work for many years.
During the exciting tour of Kiev, the conference participants stood for a
minute of silence near the newly opened memorial plaque on the house where
M. Krawtchouk lived and where he was arrested on February 21, 1938.
The 9th Krawtchouk Conference will take place in 2002 - the 110th
anniversary of the birth of M. Krawtchouk. All the necessary information will
appear on the Krawtchouk Polynomials Home Page:
http://www.isir.minsk.by/~zelenkov/physmath/kr_polyn
Topic #10 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: Manuel Alfaro
Subject: Jose J. (Chicho) Guadalupe (1946 - 2000)
(From the Activity Group's June Newsletter)
Prof. Jose Javier Guadalupe (Chicho) died on April 1, 2000 at the age of
54 in a car accident. He was born in Santa Cruz de la Palma (Canary
Islands) and studied at the University of Zaragoza, Spain. He worked at
the University of Zaragoza (1970-1992) and the University of La Rioja
(1992-2000).
Chicho was a student of Jose Luis Rubio de Francia under whose supervision
he prepared his Ph.D. on "Closure in L^p(\mu) of analytical polynomials in
the unit circle" at the University of Zaragoza.
His general area of research was harmonic analysis. His early work was on
closure of analytical polynomials on weighted Jordan curves. Later he
worked on Fourier series in orthogonal polynomials and special functions.
Recently, he was interested in Stieltjes polynomials and varying measures.
He was a very active man, and an organizer of mathematical activities.
In the field of orthogonal polynomials and special functions, Chicho
promoted the idea of having a series of Spanish Symposia Symposia of
Orthogonal Polynomials and Applications. The first Symposium was organized
by him in Logrono in 1983.
His death is a great loss for his colleagues and mainly for Spanish people
working on orthogonal polynomials and special functions.
(Editor's Note: The Summer School "Orthogonal Polynomials and Special
Functions" to be held in Laredo, July 24-28, 2000 (OP-SF NET 6.6, Topic
#3) is to be dedicated to the memory of Chico Guadalupe.)
Topic #11 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: Daniel Lozier
Subject: Authors Selected for NIST Digital Library Project
The National Institute of Standards and Technology (NIST) has selected
authors for the following chapters of the Digital Library of
Mathematical Functions (DLMF):
Mathematical and Physical Constants. NIST.
Algebraic and Analytical Methods. R. Askey & R. Roy.
Asymptotic Approximations. F. Olver & R. Wong.
Numerical Methods. C. Brezinski & W. Gautschi.
Computer Algebra. P. Paule & F. Chyzak.
Elementary Functions. S. Krantz.
Gamma Function. R. Askey.
Exponential Integral, Logarithmic
Integral, Sine and Cosine Integrals. N. Temme.
Error Functions, Dawson's Integral,
Fresnel Integrals. N. Temme.
Incomplete Gamma Functions and
Generalized Exponential Integral. R. Paris.
Airy and Related Functions. F. Olver.
Bessel Functions. F. Olver & L. Maximon.
Struve Functions and Anger-Weber Functions. R. Paris.
Confluent Hypergeometric Functions. J. Wimp.
Coulomb Wave Functions. M. Seaton.
Parabolic Cylinder Functions. N. Temme.
Legendre Functions and Spherical Harmonics. M. Dunster.
Hypergeometric Functions. A. Olde Daalhuis.
Generalized Hypergeometric Functions
and Meijer G-Function. R. Askey.
q-Hypergeometric Functions. G. Andrews.
Classical Orthogonal Polynomials. R. Koekoek & R. Swarttouw.
Other Orthogonal Polynomials. R. Koekoek & R. Swarttouw.
Elliptic Integrals. B. Carlson.
Jacobian Elliptic Functions and
Theta Functions. P. Walker & W. Reinhardt.
Weierstrass Elliptic Functions. P. Walker & W. Reinhardt.
Bernoulli and Euler Numbers and Polynomials. K. Dilcher.
Zeta and Related Functions. T. Apostol.
Combinatorial Analysis. D. Bressoud.
Functions of Number Theory. T. Apostol.
Statistical Methods and Distributions. I. Olkin & D. Kemp.
Mathieu Functions and Hill's Equation. G. Wolf.
Lame Functions. Spheroidal Wave Functions. H. Volkmer.
Heun Functions. B. Sleeman & V. Kuznetsov.
Painleve Transcendents. P. Clarkson.
Integrals with Coalescing Saddles. M. Berry & C. Howls.
Wavelets. G. Strang.
3j, 6j, 9j Symbols. L. Maximon.
This list is subject to change, and all chapters are subject to editorial
review and independent validation before acceptance by NIST. Contracts are
in process now with some of the authors, and are impending for the others.
The work is being organized and supervised by 4 NIST editors and 10 associate
editors from other institutions.
The NIST editors and their areas of responsibility are: D. Lozier
(General), F. Olver (Mathematics), C. Clark (Scientific Applications), and
R. Boisvert (Information Technology).
The associate editors and their areas of responsibility are: R. Askey
(special functions), M. Berry (physics), W. Gautschi (numerical analysis),
L. Maximon (physics), M. Newman (combinatorics and number theory), I.
Olkin (statistics), P. Paule (computer algebra), W. Reinhardt (chemistry),
N. Temme (special functions), and J. Wimp (special functions).
The DLMF is being modeled after the 1964 National Bureau of Standards
Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, editors.
It is being prepared on the basis of a thorough review of the published
archival literature, with emphasis on the presentation of those
mathematical properties that are most useful in scientific and other
applications. It will include computational information, pointers to
software, illustrative applications, and graphics. It will be disseminated
from a Web site at NIST with capabilities for browsing, searching,
interactive visualization, and importation of information into documents
or computer programs. Also, a book will be published with a CD-ROM that
will reproduce many of the capabilities of the Web site. Funding has been
provided by the National Science Foundation. Completion is due in 2003.
Further information can be found at the project Web site,
http://dlmf.nist.gov.
See also http://dlmf.nist.gov/about/publications.
Topic #12 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: Walter Van Assche
Subject: Special Functions Posters
Wolfram Research has prepared a major poster on special functions.
It is divided into five distinct panels:
Elliptic functions
Elementary functions
Hypergeometric functions
Zeta and other functions
Special function (general)
For details and pictures of these posters one can visit
http://www.specialfunctions.com
Topic #13 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: OP-SF preprints in xxx archive
The following preprints related to the field of orthogonal polynomials and
special functions were recently posted or cross-listed to one of the
subcategories of the xxx archives. See:
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
Article math.CA/0005095
Title: A generalization of Kummer's identity
Author: Raimundas Vidunas
From: Raimundas Vidunas
Article math.QA/0005071
Title: The q-twisted cohomology and the q-hypergeometric
function at |q|=1
Author: Yoshihiro Takeyama
From: Yoshihiro Takeyama
Article math.QA/0005123
Title: Refined q-trinomial coefficients and character identities
Author: S. Ole Warnaar
From: S. Ole Warnaar
Nonlinear Sciences, abstract nlin.SI/0007001
From:
Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on
HyperElliptic Sigma Functions
Author: Shigeki Matsutani
Nonlinear Sciences, abstract nlin.SI/0005064
From: Peter Forrester
Painlev\'e transcendent evaluation of the scaled distribution of the smallest
eigenvalue in the Laguerre orthogonal and symplectic ensembles
Author: P.J. Forrester (University of Melbourne)
Topic #14 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Changes of address, WWW pages, etc.
Damian G. McGuckin informs us of teh following new contact information.
Address:
Pacific ESI, Unit 22
8 Campbell St, Artarmon N.S.W 2064, Australia
Phone: 61-2-9906-3377
Fax: 61-2-9906-3468
Email: damianm@esi.com.au
Topic #15 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: About the Activity Group
The SIAM Activity Group on Orthogonal Polynomials and Special Functions
consists of a broad set of mathematicians, both pure and applied. The
Group also includes engineers and scientists, students as well as experts.
We have around 140 members scattered about in more than 20 countries.
Whatever your specialty might be, we welcome your participation in this
classical, and yet modern, topic. Our WWW home page is:
http://math.nist.gov/opsf/
This is a convenient point of entry to all the services provided by the
Group. Our Webmaster is Bonita Saunders (bonita.saunders@nist.gov).
The Activity Group sponsors OP-SF NET, which is transmitted periodically
by SIAM. It is provided as a free public service; membership in SIAM is
not required. The OP-SF Net Editor is Martin Muldoon (muldoon@yorku.ca).
To receive the OP-SF NET, send your name and email address to
poly-request@siam.org.
Back issues can be obtained by anonymous ftp from ftp.wins.uva.nl in the
directory:
pub/mathematics/reports/Analysis/koornwinder/opsfnet.dir
or at the WWW addresses:
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http://math.nist.gov/opsfnet/archive
The NET provides fast turnaround compared to the printed Newsletter, also
sponsored by the Activity Group, and edited by Renato Alvarez-Nodarse and
Rafael Yanez. It appears three times a year and is mailed by SIAM. Back
issues are accessible at:
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To receive the Newsletter, you must be a member of SIAM and of the
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For current information on SIAM and Activity Group membership, contact:
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Finally, the Activity Group operates an email discussion group, called
OP-SF Talk. To subscribe, send the email message
subscribe opsftalk Your Name
to listproc@nist.gov. To contribute an item to the discussion, send
email to opsftalk@nist.gov. The archive of all messages is accessible
at:
http://math.nist.gov/opsftalk/archive
Topic #16 ------------ OP-SF NET 7.4 ------------- July 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Submitting contributions to OP-SF NET and Newsletter
To contribute a news item to OP-SF NET, send email to poly@siam.org with a
copy to the OP-SF Editor. Please note that submissions to the Net are
automatically considered for the Newsletter, and vice versa, unless the
contributor requests otherwise.
Contributions to the OP-SF NET 7.5 should be sent by September 1, 2000.
Please send your Newsletter contributions directly to the Editors:
Renato Alvarez-Nodarse
Departamento de Analisis Matematico
Universidad de Sevilla
Apdo. Postal 1160,
Sevilla E-41080 Spain
fax: +34-95-455-7972
e-mail: renato@gandalf.ugr.es
ran@cica.es
Rafael J. Yanez
Departamento de Matematica Aplicada
Universidad de Granada
E-18071 Granada, Spain
phone: +34-58-242941
fax: +34-58-242862
e-mail: ryanez@ugr.es
preferably by email, and in latex format. Other formats are also
acceptable and can be submitted by email, regular mail or fax.
The deadline for submissions to be included in the October 2000 issue is
September 15, 2000 and for the February 2001 issue it is January 15, 2001.
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OP-SF NET is a forum of the SIAM Activity Group on
Special Functions and Orthogonal Polynomials.
We disseminate your contributions on anything of interest to the
special functions and orthogonal polynomials community. This
includes announcements of conferences, forthcoming books, new
software, electronic archives, research questions, job openings.
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The elected Officers of the Activity Group (1999-2001) are:
Daniel W. Lozier, Chair
Walter Van Assche, Vice Chair
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The appointed officers are:
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