O P - S F N E T Volume 8, Number 2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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. Planned activities (Activity Group Chair)
2. Request for Information for DLMF Project
3. opsftalk
4. Delft Workshop on Quantum Groups and Special Functions
5. Workshop on Advanced Special Functions in Italy
6. Benin Workshop on Mathematical Physics
7. IMA Program on "Special Functions in the Digital Age"
8. Report on AMADE-2001
9. Book by Dunkl and Xu on Orthogonal Polynomials of Several
Variables
10. Book on Orthogonal Polynomial for Exponential Weights
11. Book by Schoutens on Stochastic Processes and Orthogonal
Polynomials
12. Further information on the Hong Kong Proceedings
13. Maple packages for hypergeometric summation
14. OP-SF preprints in xxx archive
15. Changes of Address, WWW pages, etc.
16. About the Activity Group
17. Submitting contributions to OP-SF NET and Newsletter
Calendar of Events:
2001
April 9: Workshop on Quantum Groups and Special Functions,
Delft, The Netherlands 8.2 #4
April 17-20: Conference "Applications of the Macdonald Polynomials",
Newton Institute, Cambridge, UK 7.5 #2, 8.1 #2
June 18-22: Symposium on Orthogonal Polynomials, Special Functions and
Applications, Rome, Italy 7.3 #2, 8.1 #3
June 24-29: Workshop on "Advanced Special Functions and Related
Topics in Probability and in Differential Equations",
Melfi, Italy 8.2 #5
June 25 - July 6: Workshop "The Macdonald Polynomials",
Newton Institute, Cambridge, UK 7.5 #2
July 2-12: Summer School on Applied Analysis, Hong Kong 7.5 #3
July 9-13: SIAM Annual Meeting, San Diego, California, USA
See: http://www.siam.org/meetings/an01/
July 9-22: Summer School in Asymptotic Combinatorics,
St. Petersburg, Russia 7.6 #3
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
October 28 - November 2: Workshop on Mathematical Physics,
Porto-Novo, Benin 8.2 #6
2002
July 22 - August 2: IMA Summer Program "Special Functions in the
Digital Age" Minneapolis, Minnesota, USA 8.2 #7
August 5-14: Workshop on Special Functions at FoCM'02, "Foundations of
Computational Mathematics" Minneapolis,
Minnesota, USA 8.1 #1
Future plans:
* There are plans to organize summer schools on "Orthogonal Polynomials and
Special Functions" in Europe during the coming three years:
- 2001 (probably September): in Germany (contact person: Rupert Lasser
)
- 2002 : in the Netherlands or Belgium (contact person: Erik Koelink
- 2003 (time undecided): in Portugal (contact person: Amilcar
Branquinho).
The coordinator of the three summer schools is Erik Koelink
(koelink@dutiaw4.twi.tudelft.nl). These summer schools are part of our
Activity Group's scientific program. The scientific committee consists of
Erik Koelink, Rupert Lasser, Amilcar Branquinho, Paco Marcellan and Walter
Van Assche.
Topic #1 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: Daniel Lozier
Subject: Planned activities
1. SIAG OP-SF Summer Schools. The first of these was held at Laredo,
Spain, July 24-28, 2000. Three more are planned: September 2001 in
Germany, 2002 in Belgium, and 2003 in Portugal. Paco Marcellan and
Walter Van Assche, our Program Director and Vice Chair, are leading the
organizing committee for these events.
2. Sixth International Symposium on Orthogonal Polynomials, Special
Functions, and Applications (OPSFA), Rome, Italy, June 18-22, 2001. The
7-member organizing committee includes 3 SIAG members (De Bruin,
Marcellan, Muldoon). Of 8 invited speakers, 5 are SIAG members (Askey,
Dunkl, Suslov, Temme, Van Assche). All SIAG officers will be present at
this Symposium, and I plan to hold the 2001 officer's meeting there.
Also, if additional SIAG members plan to be in Rome, please let me know
in advance. If there are enough of us, it might be worthwhile to have
a general member's meeting in Rome.
3. SIAM Annual Meeting, July 9-13, 2001. We have decided not to sponsor a
minisymposium because recent annual meetings have not attracted our
membership or, indeed, our officers. There are a variety of reasons for
this, not least the existence each year of at least one meeting - and
usually more than one - on orthogonal polynomials and special functions in
the U.S. and abroad. Naturally, our members tend to use their limited
travel budgets to attend meetings that are closely connected with their
research. It doesn't help that our subject area has not been
well-represented on the plenary programs at recent SIAM meetings. I am
trying to open a dialog with SIAM about these problems. One idea is to
ask SIAM to appoint a representative of our SIAG to be on the organizing
committee for the 2002 annual meeting. This meeting will celebrate the
50th anniversary of SIAM in Philadelphia, the home city of SIAM. Another
idea is SIAM/SIAG co-sponsorship of non-SIAM meetings. I hope further
ideas will come from officers and members at the OPSFA meeting in Rome or
by email to me.
Topic #2 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: Daniel Lozier
Subject: Request for Information for DLMF Project
[This was sent to opsftalk on March 5, 2001]
DLMF Editor's Note: The Web site for the DLMF (Digital Library of Mathematical
Functions) is http://dlmf.nist.gov. For a long time the information there was
very limited but that is beginning to change. Authors are writing chapters, and
as these take shape details are being posted at the Web site.
The DLMF will include selected typical applications of the various special
functions, especially in physics. The following message from Dick Askey, a DLMF
author as well as a DLMF Associate Editor, asks the readers of this list to help
by providing examples. Please send them to opsftalk@nist.gov. For information
about the OPSF-Talk List Service and access to the OPSF-Talk Archive, see
http://math.nist.gov/opsf.
I am general editor for the DLMF project. The other primary editors are Frank
Olver (mathematics), Charles Clark (scientific applications), and Ron Boisvert
(information technology). The associate editors are named at the Web site.
Dan Lozier
From: Richard Askey
Subject: Request for information
As many of you know, NIST is doing a revision of the Handbook of
Mathematical Functions, now titled "The digital library of mathematical
functions". In addition to including important facts about many special
functions, there is a need to include references to uses of them. Each of
us knows some, but collectively we know much more. It would be useful to
the authors of the individual chapters if people sent examples of
important uses of the usual special functions and their properties.
Let me give an example of how an old handbook was used to suggest an
interesting property of Legendre polynomials, and then mention a use of
the inequalities which were suggested by one graph in Jahnke and Emde.
When Legendre polynomials are graphed on (-1,1) a number of things are
suggested. First, all the zeros lie in this interval. Second, the
polynomials are bounded by 1 in absolute value on this interval. Third, if
the absolute values of the successive extrema are considered, they
decrease when going from 1 to 0. All of these facts had been observed and
proved more than 100 years ago. About 55 years ago, John Todd looked
carefully at a graph consisting of P_n(x) on (0,1) for n=1,2,...7. He
noticed that the first minimum value of each of these functions when you
look back from 1 seems to be an increasing function of n, the first
maximum seems to be decreasing, and so on. These extrema have limits of
the extrema of the Bessel function J_0(x). In a few years a proof was
found by Gabor Szego, extended to ultraspherical polynomials suitably
normalized by Otto Szasz, and a similar result was found for Hermite
polynomials when suitably normalized. For many years these inequalities
sat there as beautiful results but without serious use.
The result for Legendre polynomials was rediscovered by Cornille and
Martin in some work on pi-pi scattering. They also found a different
weighted result for ultraspherical polynomials. Between the publication of
their first paper and their second, someone told them of Szego's work.
References are given in my SIAM regional conference lectures. It would
have helped Cornille and Martin if this result had been included in a book
they looked at. As we all know, results which are not eventually
published in a book are very likely to get lost. Also, users of special
functions will find it helpful to know the general areas in which these
functions are used. Finally, mathematicians need to know about the uses
of the functions since the users frequently need something just a little
bit different than what mathematicians have done.
There is another graph in Jahnke and Emde which was not looked at for
even longer. This is a graph of Q_n(x) on (0,1) for n=1,2,3,4,5. A
similar monotonicity result is suggested by this graph, and has been
proven. I don't know applications of it, but strongly suspect there will
be some.
I am writing the chapters on gamma and beta functions and on higher
hypergeometric series. Any references which can be sent about uses of
these functions would be helpful. I am sure that the other authors would
also find it useful to hear about applications of the functions they are
writing about. To avoid duplication, it would be best to send them to the
list opsftalk@nist.gov and Dan Lozier can forward them the author of the
chapter if necessary.
Thanks in advance for help.
Dick Askey
Topic #3 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: opsftalk
After a quiet period, there has been here a recent spurt of activity in
opsftalk, the discussion group of our Activity Group.
Sergei Sadov asked whether certain formulas arising in matrices of
potentials in the Legendre basis were known. Richard Askey pointed out a
connection with work of Polya and Szego. George Gasper pointed out that
another formulas asked about by Sadov is equivalent to a known formula of
Whipple and Sadov forwarded further references sent to him by E. D.
Krupnikov. David Strozzi asked about the numerical computation of the
hypergeometric function bringing some responses and references from
Daniel Lozier and Nico Temme.
A remarkable aspect of these exchanges was the quick turnaround time.
Readers are encouraged to subscribe and sent their questions and comments
to opsftalk. See the end of Topic #16 for details.
Topic #4 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: Erik Koelink
Subject: Delft Workshop on Quantum Groups and Special Functions
On Monday, April 9, 2001, there will be a one-day
WORKSHOP `QUANTUM GROUPS AND SPECIAL FUNCTIONS'
at the Technische Universiteit Delft.
Programme:
Hjalmar Rosengren (Goteborg, Sweden)
Special functions and dynamical quantum groups
Joris Van der Jeugt (Gent, Belgium)
Character formulas of gl(m/n), Weyl's denominator
formula and supersymmetric functions
Stefaan Vaes (Leuven, Belgium)
Extensions of locally compact quantum groups
Johan Kustermans (Delft, the Netherlands)
Quantum SU(1,1), yet another example of
non-compact locally compact quantum group
See
http://aw.twi.tudelft.nl/~koelink/9april01.html
for more information. Everybody is cordially invited.
Topic #5 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: Paolo Emilio Ricci
Subject: Workshop on Advanced Special Functions in Italy
The 3rd Workshop on "Advanced Special Functions and Related Topics in
Probability and in Differential Equations", will be held in Melfi (a small
town in the South of Italy) in the period June 24-29, 2001.
This Workshop is organized by Dr. G. Dattoli and C. Cesarano (ENEA -
Frascati, Rome), Dr. D. Sacchetti and myself (Rome University "La
Sapienza").
Prof. Dr. H.M. Srivastava (University of Victoria, Canada) will be a
keynote speaker.
If you are interested, you can take a look to the Internet page
http://www.frascati.enea.it/melfi/
Please note that the total charge for participating will be around US
$400, including the registration fee (US $200). This cost will cover the
Hotel expenses (full board) for 5 days, coffee breaks, bus transportation
from Rome to Melfi and vice-versa, the social dinner, and the Volume of
Proceedings.
If you are interested in spending some more days in Italy after the OPSFA
Symposium, please contact me or another member of the Organizing
Committee, and fill our "on line" registration form.
The Workshop hotel (Parco Eudria) is far from Melfi, and located in a very
quiet and nice place. An ideal place for relaxing and exchanging
information after the OPSFA Symposium.
Topic #6 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: Andre Ronveaux
Subject: Benin Workshop on Mathematical Physics
SECOND INTERNATIONAL WORKSHOP ON CONTEMPORARY PROBLEMS IN MATHEMATICAL
PHYSICS INSTITUT DE MATHEMATIQUES ET DE SCIENCES PHYSIQUES (IMSP),
PORTO-NOVO (BENIN). October 28th - November 2nd, 2001
The main objective of the workshop is to contribute to the development of
a critical mass of researchers in Africa in such a dynamic area as
mathematical physics. The workshop brings together specialists from
diverse topics in Theoretical and Mathematical Physics. It offers to the
international scientific community the possibility of exchanging useful
information on contemporary problems in these fields through direct
interaction. The workshop also provides young African researchers with an
opportunity to know each other and to initiate scientific cooperation.
Therefore the workshop helps to strengthen research capacity and
revitalize activities in mathematical physics in African universities.
Director: Professor M.N.Hounkonnou,(IMSP)
Coordinators :
J.P. Antoine, Université Catholique de Louvain, Louvain-la-Neuve(Belgium)
H. Capo, Université Nationale du Bénin, Cotonou, (Benin)
A. Msezane, Clark Atlanta University, Atlanta (USA)
Topics include: Coherent States, Wavelets and Geometric Methods in
Theoretical Physics Modern Physics; Field Theory, Atomic, Molecular,
Statistical Physics and Theoretical Chemistry; Functional Analysis and
Algebraic Methods for Theoretical Physics, Special Functions and
Orthogonal Polynomials.
The proceedings of the workshop will be published by World Scientific
Publishing Co. The proceedings of the First International Workshop on
Contemporary Problems in Mathematical Physics (COPROMAPH1) are available
from the same publishing house.
This second International workshop (COPROMAPH2) will be co-organized by
Prof. J. Govaerts,
Institut de Physique Nucléaire,
Université Catholique de Louvain,
2, Chemin du Cyclotron,
B-1348 Louvain-la-Neuve, Belgium,
E-mail: govaerts@fynu.ucl.ac.be
and
Prof. M N Hounkonnou,
Institut de Mathématiques et de Sciences Physiques (IMSP),
B.P. 2628
Porto-Novo, Benin,
E-mail: hounkon@syfed.bj.refer.org
The activity is open to scientists from all countries. Travel and
subsistence expenses of the participants should be covered by the home
institution. However, limited funds will be made available for scientists
from African countries. For more informations about: registration fees,
presentation of communications, lodging facilities and the city of Cotonou
please consult the web page http://www.chez.com/imspurpt/copromaph2
Topic #7 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: IMA Program on "Special Functions in the Digital Age"
The Institute for Mathematics and its Applications, Minneapolis,
Minnesota, USA, will host a summer Program "Special Functions in the
Digital Age" in the period July 22 - August 2, 2002.
The program is not yet open for registration and the schedule and list of
participants are not yet available. The following description is taken
form the web site: http://www.ima.umn.edu/digital-age/
Introduction:
Mathematical tables and handbooks have played a pivotal role in
applications and also the development of mathematics itself over the
centuries. Now, with the advent of the digital age, the traditional
handbook format has become obsolete, and a complete rethinking of the
nature and role of mathematical handbooks must be undertaken. The purpose
of this program is to formulate, though concrete examples and experiences,
the role and character of digital libraries in mathematics, and the
mathematical and applied fields that would benefit from such a library.
The first serious attempt to address these issues is the ongoing Digital
Library of Mathematical Functions (DLMF) project at the National Institute
of Standards and Technology (NIST). This workshop will take the DLMF
project as a basis for assessing both the state of the art in special
function theory, what aspects are of importance in applications,
particularly to chemistry and physics, and the experiences gained in this
project to formulate recommendations for how digital libraries of
mathematics should be organized, utilized, and developed. We also
anticipate the experiences of the DLMF project to provide insight and
recommendations for how mathematics should be stored and disseminated over
the internet.
Of the currently used handbooks, the most well-developed have been those
devoted to special functions and their applications. The principal
handbooks on special functions, "Higher Transcendental Functions" (the
Bateman Project) and the NIST (formerly National Bureau of Standards)
"Handbook of Mathematical Functions," are among the most useful, widely
consulted technical volumes ever published, but they are now out of date,
due to rapid research progress and revolutionary changes in technology.
(See http://www.siam.org/siamnews/03-98/function.htm for additional
information.) Using these as concrete examples of a mathematical digital
library, the program will assess recent progress in updating these
handbooks and recent advances in the theory and use of special functions,
and to point out the areas of research in special functions that hold the
most promise and importance for future development, both for theorists and
users. In the broader arena, the workshop will aim to use the experience
in this particular subject to generate recommendations for further digital
library projects in the mathematical sciences and their applications,
including, but not limited to, numerical analysis, group theory, signal
processing, statistics, linear algebra, partial differential equations,
and so on.
Description:
The IMA workshop will use the DLMF project as a foundation and discuss
what more should be done, what areas are incomplete or unrepresented, what
are the resulting mathematical, symbolic, numerical and web issues,
applications in physics, chemistry, etc., relationships with the Bateman
project, and potential for other digital libraries in other mathematical
areas. The workshop is to have a very broad outlook, encompassing a wide
range of subjects connected with special functions, as well as issues
concerning digital libraries and the delivery of mathematics over the
internet.
A major portion of this program (7 days) will be assessments of research
progress and promising vistas for future research by distinguished experts
in the areas of asymptotics, combinatorial functions, statistics, computer
algebra, algebraic and group theoretic methods, applications to the
physical sciences, orthogonal polynomials, numerical methods, zeta
functions & random matrices, Painlevé functions, elliptic functions,
elliptic hypergeometric functions and the Heun function group, with the
aim of pointing out what is of greatest importance in the theory and
applications, and what should be included in digital library projects.
The remainder of the program (3 days) will be devoted to Digital Libraries
generally and, specifically, Digital Libraries and the Mathematical
Sciences, including the delivery of mathematics over the Internet. It will
conclude with a panel on the "Future of Mathematical Digital Libraries,"
with panelists from the special functions research and users communities,
as well as representatives from mathematics societies and government
funding agencies.
There will be several discussion sessions to develop specific
recommendations for special function topics to be included in future
Digital Libraries in Mathematics. Also there will be poster sessions, and
several software demonstrations (particularly of computer algebra and
numerical packages for special functions), and much of the software will
be available during the program for informal use by participants. This
program will link with special function related sessions at the
Foundations of Computational Mathematics (FoCM'02) meeting that will be
hosted by the IMA, August 5-15, 2002.
The program is meant for researchers in the theory and computation of
special functions (definitely including people new to the field who are
looking for the most promising areas for future research), for users of
special functions, and for persons interested in the delivery of
mathematics over the Internet.
Topic #8 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: Anatoly Kilbas and Sergei Rogosin
Subject: Report on AMADE-2001
International Conference "Analytical Methods of Analysis and Differential
Equations" (AMADE-2001), Minsk, Belarus, February 15-19, 2001
The international conference "Analytical Methods of Analysis and
Differential Equations" (AMADE-2001) took place February 15-19, 2001 in
Minsk, Belarus. It continues the series of the international conferences
"Boundary Value Problems, Special Functions and Fractional Calculus"
devoted to the 90th birthday of academician F.D.Gakhov (Minsk, Belarus,
February 15-20, 1996), and "Analytical Methods of Analysis and
Differential Equations" (AMADE) (Minsk, Belarus, September 14-18, 1999).
AMADE-2001 was organized by the Belarusian State University, the
Belarusian National Academy of Sciences together with Moscow State
University. It was held at the Olympic Sport Center "Staiki" which is
situated 10 km from Minsk, the capital of Belarus.
262 mathematicians from 21 countries confirmed their interest in the
Conference. Abstracts of their reports were published in "Abstracts of
AMADE-2001". 138 scientists from Algeria, Belarus, France, Germany, Great
Britain, Italy, Kasakhstan, Kuwait, Lithuania, Macedonia, Poland, Russia,
Ukraine and Yugoslavia took part in AMADE-2001.
The work of the conference was divided into four sections:
1. Integral transforms and special functions.
2. Differential equations and applications.
3. Integral, difference, functional equations and fractional calculus.
4. Real and complex analysis.
There were 20 plenary invited lectures and 124 sectional talks devoted to
different problems of analysis and differential equations.
Plenary invited lectures were given by the following mathematicians:
Antonevich A.B. (Minsk, Belarus) Homogeneous Banach algebras
and algebraic fibering
Begehr H. (Berlin, Germany) Orthogonal decompositions in $L_2$
Burenkov V.I. (Cardiff, UK) Equivalence of embedding theorems for Sobolev
spaces to some spectral properties of Neumann Laplacian
Volovich I.V. (Moscow, Russia), Radyno Ja.V. (Minsk, Belarus), Khrennikov À.Ju.
(Vaxjo, Sweden) Operator of multiplication on the group of adels
Vu Kim Tuan (Kuwait) The Paley-Wiener theorem for Sturm-Liouville transform
Glaeske H.-J. (Jena, Germany) On a Hermite transform in spaces of generalized
functions on $R^n$
Gromak V.I. (Minsk, Belarus) Discrete Painleve equations of the high order
Dzhenaliev M.T., Ramazanov M.I. (Almaty, Kazakhstan) On loaded equations with
periodic boundary conditions
Galkowski K. (Z.Gora, Poland), Owens D.H. (Sheffield,UK) Control problems for
a class of 2d repetitive systems
Kakichev V.A. (Novgorod, Russia) Convolution of the Borel transform
Karapetyants N.K. (Rostov-on-Don, Russia) On a statement of the problem for
equations with fractional-linear shift on the axes
Kilbas A.A. (Minsk, Belarus) Some aspects of the theory of differential and
integral equations of fractional order
Lanza de Cristoforis M., Lamberti P.D. (Padova, Italy) An analyticity theorem
for symmetric functions of the eigenvalues of a compact self-adjoint
operator
Laurinchikas À. (Vilnius, Lituania) The universality of certain zeta function
Marti J.-A. (Guadeloupe, France) On some characteristics of Cauchy problems
Minyuk S.A. (Grodno, Belarus), Metelskii À.V. (Minsk, Belarus) On
completeness of linear systems with a delay
Mityushev V.V. (Slupsk, Poland) Problem of R-linear conjugation and its
applications in mechanics of composite materials
Rogosin S.V. (Minsk, Belarus) On complex variable approach for moving
boundary value problems
Yurchuk N.I., Baranovskaya S.N., Yashkin V.I. (Minsk, Belarus) On the
classic and the weakened solutions of hyperbolic equations of even
order
February 19th, 2001 was a day in memory of academician F.D.Gakhov
(1906-1980), the founder of Belarusian school on boundary value problems
and singular integral equations. His former students and successors gave
talks.
Participants remarked on the high scientific level of the conference.
The Proceedings of AMADE-2001 will be published in special issues of the
Journal "Proceedings of Institute of Mathematics" of the Belarusian
National Academy of Sciences. Some of the reports were recommended for
publication in the Journal "Integral Transforms and Special Functions".
Topic #9 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Book by Dunkl and Xu on Orthogonal Polynomials of Several Variables
[From the web site: http://www.cambridge.org]
Title: Orthogonal Polynomials of Several Variables
Authors: Dunkl, Charles and Xu, Yuan
April 2001, 400 Pages, Hardback, ISBN: 0-521-80043-9, $80.00
This is the first modern book on orthogonal polynomials of several
variables, which are valuable tools used in multivariate analysis,
including approximations and numerical integration. The book presents the
theory in elegant form and with modern concepts and notation. It
introduces the general theory and emphasizes the classical types of
orthogonal polynomials whose weight functions are supported on standard
domains such as the cube, the simplex, the sphere and the ball. It also
focuses on those of Gaussian type, for which fairly explicit formulae
exist. The authors' approach blends classical analysis and
symmetry-group-theoretic methods. The book will be welcomed by research
mathematicians and applied scientists, including applied mathematicians,
physicists, chemists and engineers.
SERIES NAME:
Encyclopedia of Mathematics and its Applications
SUBJECT:
Mathematics - analysis, probability
Topic #10 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Book on Orthogonal Polynomial for Exponential Weights
[From the Springer Mathematics Newsletter]
Forthcoming:
A.L. Levin, The Open University of Israel, Tel Aviv, and
Doron S. Lubinsky, Witwatersrand University, Wits, South Africa
Orthogonal Polynomial for Exponential Weights
CMS Books in Mathematics, Vol 4
2000. Approx. 350 pp. Hardcover $69.95 (tent.) ISBN 0-387-98941-2
The analysis of orthogonal polynomials associated with general weights has
been a major theme in classical analysis this century. The use of
potential theory since the early 1980's has had a dramatic influence on
the development of orthogonal polynomials associated with weights on the
real line. For many applications of orthogonal polynomials, for example in
approximation theory and numerical analysis, it is not asymptotics but
certain bounds that are most important.
In this monograph, the authors define and discuss their classes of
weights, state several of their results on Christoffel functions,
Bernstein inequalities, restricted range inequalities, and record their
bounds on the orthogonal polynomials as well as their asymptotic results.
This book will be of interest to researchers in approximation theory and
potential theory, as well as in some branches of engineering.
Topic #11 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Book by Schoutens on Stochastic Processes and Orthogonal Polynomials
[From the web site: http://www.springer-ny.com]
Stochastic Processes and Orthogonal Polynomials
Series: Lecture Notes in Statistics, Vol. 146
Wim Schoutens, Katholieke Universiteit Leuven,
B-3001 Heverlee
Price $49.95
184 pages , 6 1/8 x 9 1/4, paperback
ISBN: 0-387-95015-X, published 2000
ABOUT THIS BOOK
The book offers an accessible reference for researchers in the
probability, statistics and special functions communities. It gives a
variety of interdisciplinary relations between the two main ingredients of
stochastic processes and orthogonal polynomials. It covers topics like
time dependent and asymptotic analysis for birth-death processes and
diffusions, martingale relations for Levy processes, stochastic integrals
and Stein's approximation method. Almost all well-known orthogonal
polynomials, which are brought together in the so-called Askey Scheme,
come into play. This volume clearly illustrates the powerful mathematical
role of orthogonal polynomials in the analysis of stochastic processes and
is made accessible for all mathematicians with a basic background in
probability theory and mathematical analysis.
Wim Schoutens is a Postdoctoral Researcher of the Fund for Scientific
Research-Flanders (Belgium). He received his PhD in Science from the
Catholic University of Leuven, Belgium.
Topic #12 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Further information on the Hong Kong Proceedings
[This is from information sent by Charles Dunkl and Dan Lozier]
In connection with the Proceedings of the International Workshop on
Special Functions -- Asymptotics, Harmonic Analysis and Mathematical
Physics held June 21-25, 1999 at the City University of Hong Kong, the
following is the full bibliographic information to supplement our
announcement in OP-SF NET 7.6, Topic #5 :
Special Functions: Proceedings of the International Workshop, C. Dunkl, M.
Ismail, R. Wong, editors, 438 + xi pages, World Scientific (Singapore),
ISBN 981-02-4393-6, 2000.
There was a panel discussion at the Workshop, for which a summary was
written. This summary is mentioned in the preface to the Proceedings but
was omitted inadvertently. It can be seen at
http://math.nist.gov/opsf/books/hongkong99.html.
It appeared also in OPSF-NET 6.5, Topic # 7 (September 1999) and in the
printed Newsletter (vol. 10, no. 1, October 1999).
For further information about the Workshop, including photographs, see
http://www.cityu.edu.hk/ma/conference/iwsf/index.html.
Topic #13 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: Wolfram Koepf
Subject: Maple packages for hypergeometric summation
Updates of the Maple packages hsum.mpl and qsum.mpl for hypergeometric
summation and q-hypergeometric summation [see my book "Hypergeometric
Summation", Vieweg, Braunschweig, 1988, distributed in the North America
by the AMS, see http://www.ams.org/bookstore, reviewed in OP-SF NET 6.4
#12] can be obtained from the web page
http://www.mathematik.uni-kassel.de/~koepf/Publikationen.
The updates work now with Maple V and Maple 6, and the names of the
updated versions are hsum6.mpl and qsum6.mpl. They contain implementations
of Gosper's, Zeilberger's and Petkovsek's algorithms and their
corresponding q-versions.
Topic #14 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: OP-SF preprints in xxx archive
The following preprints related to the fields of orthogonal polynomials
and special functions were recently posted or cross-listed to one of the
subcategories of the xxx archives. See especially:
http://front.math.ucdavis.edu/math.CA
http://front.math.ucdavis.edu/math.CO
http://front.math.ucdavis.edu/math.QA
http://xxx.lanl.gov/archive/solv-int
math.RT/0101006
Title: A generating function for the trace of the Iwahori-Hecke
algebra
Authors: Eric M. Opdam
Subj-class: Representation Theory
MSC-class: 20C08, 22D25, 22E35
math.RT/0101007
Title: On the spectral decomposition of affine Hecke algebras
Authors: Eric M. Opdam
Subj-class: Representation Theory
MSC-class: 20C08, 22D25, 22E35, 43A32
math.CA/0101011
Title: Some divergent trigonometric integrals
Authors: Erik Talvila
Comments: to appear in a slightly different version in Amer. Math.
Monthly
Subj-class: Classical Analysis
MSC-class: 26A42
math.CA/0101012
Title: Necessary and sufficient conditions for differentiating under
the
integral sign
Authors: Erik Talvila
Subj-class: Classical Analysis
MSC-class: 26A39
math.CA/0101013
Title: Rapidly growing Fourier integrals
Authors: Erik Talvila
Subj-class: Classical Analysis
MSC-class: 42A
math.CA/0101065
Title: Bessel Integrals and Fundamental Solutions for a Generalized
Tricomi Operator
Authors: J. Barros-Neto, Fernando Cardoso
Subj-class: Classical Analysis; Analysis of PDEs
MSC-class: 35M10 (primary) 46F10, 42B10 (secondary)
math.CA/0101073
Title: A proof of a multivariable elliptic summation formula
conjectured by Warnaar
Authors: Hjalmar Rosengren
Comments: 10 pages
Subj-class: Classical Analysis; Quantum Algebra
MSC-class: 33D67; 33E05
math.CA/0101105
Title: Orthogonal Polynomials in Analytical Method of Solving
Differential Equations Describing Dynamics of Multilevel Systems
Authors: V.A.Savva, V.I.Zelenkov, A.S.Mazurenko
Comments: 8 pages, latex, no figures, see also this http URL and this
http URL
Subj-class: Classical Analysis; Dynamical Systems
MSC-class: 33C48; 34C25
Journal-ref: Integral Transforms and Special Functions, 2000, Vol. 10,
No. 3--4, pp. 299-308
math.AP/0101113
Title: Fundamental Solutions for the Tricomi Operator, II
Authors: J. Barros-Neto, Israel M. Gelfand
Subj-class: Analysis of PDEs; Classical Analysis
MSC-class: 35M10; 33C05
math.CA/0101125
Title: Duality of orthogonal polynomials on a finite set
Authors: Alexei Borodin
Comments: AMSTeX, 9 pages
Subj-class: Classical Analysis; Probability Theory
math.QA/0101136
Title: Special functions, conformal blocks, Bethe ansatz, and SL(3,Z)
Authors: G. Felder, A. Varchenko
Comments: 10 pages, AMSLaTeX
Subj-class: Quantum Algebra; Mathematical Physics
MSC-class: 81T40; 33C67
math.CA/0101168
Title: On the sums Sum((4k+1)^(-n),k,-inf,+inf)
Authors: Noam D. Elkies
Comments: 13 pages. Written partly as an expository paper, and thus
at somewhat greater length than would be appropriate for a purely
research article on this material. Revised to correct minor errors:
typos in equations (1) and (2), and an incomplete argument for Lemma
2, noticed respectively by Paul Krapivsky and Robin Chapman
Subj-class: Classical Analysis; Combinatorics
MSC-class: 11B68 (Primary) 05A15 (Secondary)
math.QA/0101178
Title: q-Analogues for Green functions for powers of the invariant
Laplacian in the unit disc
Author: D. Shklyarov
Comments: LaTeX 2e, 18 pages, vaksman@ilt.kharkov.ua
Subj-class: Quantum Algebra; Complex Variables; Functional Analysis
MSC-class: 81R50 (Primary) 81Q99 (Secondary)
Journal-ref: Mathematical physics, analysis, geometry (Kharkov
Mathematical Journal), v.7, 2000, p.345-365
math.CA/0101187
Title: Little q-Legendre polynomials and irrationality of certain
Lambert series
Authors: Walter Van Assche
Comments: 15 pages
Subj-class: Classical Analysis; Number Theory
MSC-class: 33D45; 11J82
math.CA/0101188
Title: Multiple orthogonal polynomials associated with Macdonald
functions
Authors: W. Van Assche, S.B. Yakubovich
Comments: 13 pages
Subj-class: Classical Analysis
MSC-class: 33C10; 42C05
Journal-ref: Integral Transforms and Special Functions 9 (2000),
229-244
math.QA/0101216
Title: Generalized Hermite polynomials
Author: Vadim V. Borzov
Comments: 15 pages, no figures
Subj-class: Quantum Algebra; Classical Analysis
MSC-class: 05E35 (Primary) 05E35 (Secondary)
math.QA/0101259
Title: The integral representations of the q-Bessel-Macdonald
functions
Authors: V.-B.K. Rogov
Comments: 10 pages, Latex
Subj-class: Quantum Algebra
MSC-class: 22Exx
cond-mat/0101464
Title: Solution of a Generalized Stieltjes Problem
Authors: B. Sriram Shastry, Abhishek Dhar
Comments: 19 pages, 4 figures
Subj-class: Condensed Matter; Exactly Solvable and Integrable
Systems; Mathematical Physics; Classical Analysis
math.GM/0102031
Title: Riemann hypothesis and Superconformal Invariance
Authors: Matti Pitkanen
Comments: 17 pages, addition of new material about realization of
superconformal symmetry
Subj-class: General Mathematics
math.CA/0102032
Title: Analytic continuation of the generalized hypergeometric series
near unit argument with emphasis on the zero-balanced series
Authors: Wolfgang Buehring, H. M. Srivastava
Comments: 19 pages
Subj-class: Classical Analysis
MSC-class: 33C20, 34E05 (Primary) 41A58 (Secondary)
Journal-ref: Themistocles M. Rassias (Editor), Approximation Theory
and Applications, Hadronic Press, Palm Harbor, FL 34682-1577, U.S.A.,
ISBN 1-57485-041-5, 1998, pp. 17-35
math.CO/0102073
Title: Variants of the Andrews-Gordon Identities
Authors: A. Berkovich, P. Paule
Comments: 12 pages, 1 figure
Subj-class: Combinatorics; Number Theory; Quantum Algebra
MSC-class: 05A10, 05A19, 11B65, 11P82
math.CO/0102106
Title: A computer proof of a polynomial identity implying a partition
theorem of Goellnitz
Authors: A. Berkovich, A. Riese
Comments: 12 pages, to appear in Adv. Appl. Math
Subj-class: Combinatorics; Number Theory; Quantum Algebra
MSC-class: 05A19, 05A30, 11P82, 33F10
math.CA/0102111
Title: Hermite functions and uncertainty principles for the Fourier
and the windowed Fourier transforms
Authors: Aline Bonami, Bruno Demange, Philippe Jaming
Comments: 22 pages, submitted
Subj-class: Classical Analysis; Mathematical Physics
MSC-class: 42B10;32A15;94A12
hep-th/0102039
Title: A_N-type Dunkl operators and new spin Calogero-Sutherland
models
Authors: F. Finkel, D. Gomez-Ullate, A. Gonzalez-Lopez, M.A.
Rodriguez, R. Zhdanov
Comments: 18 pages. Typeset using LaTeX with amslatex and revtex 4
packages
Subj-class: High Energy Physics - Theory; Mathematical Physics;
Exactly Solvable and Integrable Systems
math-ph/0102007
Title: On the Motion of Zeros of Zeta Functions
Authors: Hans Frisk, Serge de Gosson
Comments: 11 pages, 3 figures (better image resolution available on
this http URL)
Subj-class: Mathematical Physics
MSC-class: 11M06
math-ph/0102020
Title: Laplace transform of spherical Bessel functions
Authors: A. Ludu, R. F. O'Connell
Comments: 5 pages LATEX, no figures
Subj-class: Mathematical Physics; Algebraic Geometry
math-ph/0102026
Title: The Darboux Transform and some Integrable cases of the
q-Riccati Equation
Authors: A. Odzijewicz, A. Ryzko
Comments: 11 pages LATEX
Subj-class: Mathematical Physics
nlin.SI/0101056
Title: A Determinant Formula for a Class of Rational Solutions of
Painlev\'e V Equation
Authors: Tetsu Masuda, Yasuhiro Ohta, Kenji Kajiwara
Comments: 17 pages
Subj-class: Exactly Solvable and Integrable Systems
nlin.SI/0102020
Title: Special Functions of the Isomonodromy Type, Rational
Transformations of Spectral Parameter, and Algebraic Solutions of
the Sixth Painlev\'e Equation
Author: A. V. Kitaev
Comments: 13 pages
Subj-class: Exactly Solvable and Integrable Systems
hep-th/0102180
Title: Unitary representations of $U_{q}(\mathfrak{sl}(2,\RR))$, the
modular double, and the multiparticle q-deformed Toda chains
Authors: S. Kharchev, D. Lebedev, M. Semenov-Tian-Shansky
Comments: AmsLatex, 41 pages, 3 figures
Subj-class: High Energy Physics - Theory; Quantum Algebra; Exactly
Solvable and Integrable Systems
Topic #15 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Changes of Address, WWW pages, etc.
Grigori Olshanski writes to inform us that his private email address
olsh@glasnet.ru will be cancelled soon. Please note the new address:
olsh@online.ru
You can also use his official address
olsh@iitp.ru
Topic #16 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
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 at the WWW addresses:
http://turing.wins.uva.nl/~thk/opsfnet
http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html
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:
http://www.mathematik.uni-kassel.de/~koepf/siam.html
To receive the Newsletter, you must be a member of SIAM and of the
Activity Group. SIAM has several categories of membership, including
low-cost categories for students and residents of developing countries.
For current information on SIAM and Activity Group membership, contact:
Society for Industrial and Applied Mathematics
3600 University City Science Center
Philadelphia, PA 19104-2688 USA
phone: +1-215-382-9800
email: service@siam.org
WWW : http://www.siam.org
http://www.siam.org/membership/outreachmem.htm
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 #17 ------------ OP-SF NET 8.2 ---------------- March 15, 2001
~~~~~~~~~~~~~
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 8.3 should be sent by May 1, 2001.
Please send your (printed) 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 June 2001 issue is
May 15, 2001 and for the October 2001 issue it is September 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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Send submissions to: poly@siam.org
Subscribe by mailing to: poly-request@siam.org
or to: listproc@nist.gov
Get back issues from URL: http://turing.wins.uva.nl/~thk/opsfnet/
WWW home page of this Activity Group:
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Information on joining SIAM
and this activity group: service@siam.org
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The elected Officers of the Activity Group (1999-2001) are:
Daniel W. Lozier, Chair
Walter Van Assche, Vice Chair
Charles F. Dunkl, Secretary
Francisco Marcellan, Program Director
The appointed officers are:
Renato Alvarez-Nodarse and Rafael J. Yanez,
Newsletter Editors
Martin Muldoon, OP-SF NET editor
Bonita Saunders, Webmaster
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