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March 15, 2000
O P - S F N E T Volume 7, 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. New OPSF Webmaster and Website
2. Welcome to Bonita Saunders
3. Announcement of Minisymposium at SIAM Annual meeting
4. Conference on Reproducing Kernel Hilbert Spaces
5. Summer School, Trivandrum: Special functions and functions of
matrix argument
6. Maratea Conference on Functional Analysis and Approximation
Theory
7. Two questions on K_\nu
8. New Indian Society for Special Functions and Their Applications
9. Proceedings - Madrid Workshop on Orthogonal Polynomials
10. RISC-Linz Software Repository
11. SIAM Outreach Membership
12. OP-SF preprints in xxx archive
13. Changes of Address, WWW Pages, etc
14. Subscribing to OP-SF NET
15. Obtaining back issues of OP-SF NET and submitting contributions
to OP-SF NET and Newsletter
Calendar of Events:
2000
March 27-31: Workshop on Quantum Groups, Morelia, Mexico 6.5 #3
April 14-18: Workshop on Orthogonal Polynomials, Approximation and
Harmonic Analysis, Inzell, Germany 6.6 #2
April 16-21: Conference on Reproducing Kernel Hilbert Spaces,
Krakow, Poland 7.1 #4 7.2 #4
May 11-13: VIII International Krawtchouk Conference, Kiev, Ukraine 7.1 #5
May 17-20: Symposium on Trends in Approximation Theory,
Nashville, Tennessee, USA 6.5 #4
May 29 - June 9: Special Functions 2000: Current Perspective
and Future Directions, Tempe, Arizona, USA 6.5 #2, 7.1 #3
July 3-7: Alhambra 2000, a Joint Mathematical European-Arabic
Conference 6.4 #7
July 10-14: SIAM Annual Meeting in Puerto Rico including
Minisymposium on Orthogonal Polynomials and
Special Functions 7.2 #3
July 17-22: I Colloquium on Lie Theory and Applications,
Vigo, Spain 6.4 #8
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
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
November 27 - December 1: 4th International Interdisciplinary
meeting on "Symmetries and Integrability of Difference
Equations", Tokyo, Japan.
Contact persons:
J. Stasuma (satsuma@poisson.ms.u-tokyo.ac.jp) or
T. Tokihiro (toki@poisson.ms.u-tokyo.ac.jp)
2001
June 18-22: Symposium on Orthogonal Polynomials, Special Functions and
Applications, Rome, Italy
Contact: Andrea Laforgia
August 20-24: 3rd International meeting on Approximation
Theory, Dortmund, Germany
Contact: idomat@math.uni-dortmund.de
Future plans:
A conference in honor of Bill Jones' 70 th birthday will be organized
at Mesa State College in Grand Junction, Colorado. This will be
organized in the summer of 2001. The date and title will be announced
later. Contact persons are Catherine Bonan-Hamada (cbonan@mesastate.edu)
and Phil Gustafson (pgustafs@mesastate.edu).
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 7.2 ------------- March 15, 2000
~~~~~~~~~~~~~
From: Daniel Lozier
Subject: New OPSF Webmaster and Website
The long awaited transfer of the OPSF web site from York
University, Canada, to my institution is complete. Martin Muldoon,
our capable webmaster for several years, is handing the reins to
Bonita Saunders of NIST. Martin will, however, continue serving as
OPSF-Net Editor (though at some point he would like someone else to
take on this task as well).
I invite all of you to inspect the new site, as some changes have
already been made, and send any comments to me. It is located at
http://math.nist.gov/opsf
Topic #2 ------------ OP-SF NET 7.2 ------------- March 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Welcome to Bonita Saunders
I am delighted to pass the task of OP-SF Webmaster to Bonita Saunders.
Please change your links to
http://math.nist.gov/opsf
but I will keep the old link alive as long as necessary. It will contain
the link to the new page but will not be updated. Bonita is a
mathematician in the Mathematical Software Group at NIST (National
Institute of Standards and Technology) Gaithersburg, Maryland, USA. She
holds the degrees of BA (William and Mary), MS (Virginia) and PhD (Old
Dominion), all in Mathematics. She has worked in Boundary-fitted Grid
Generation, Numerical Solution of PDEs and Visualization of Special
Functions. Her e-mail address is: bonita.saunders@nist.gov
Topic #3 ------------ OP-SF NET 7.2 ------------- March 15, 2000
~~~~~~~~~~~~~
From: Pete McCoy
Subject: Announcement of Minisymposium at SIAM Annual meeting
The SIAM Activities Group on Orthogonal Polynomials and Special Functions
announces the Minisymposium
"Special Functions and Orthogonal Polynomials"
to be held at the SIAM Annual Meeting, Westin Rio Mar Beach Resort and
Country Club, Rio Grande, Puerto Rico, July 10-14, 2000.
Abstract:
The SIAM Activities Group on Orthogonal Polynomials and Special Functions
is dedicated to the promotion of basic research, the furtherance of
applications in mathematics, science and industry, and the exchange of
information between researchers and users. This minisymposium is intended
partly to provide an introduction to selected topics in these areas for
non- specialists, and partly to serve as a forum for the presentation of
recent research results.
Speakers:
Daniel W. Lozier "A New Web-Enabled Compendium of Special Functions"
Joaquin Bustoz "Fourier Series on the q-linear lattice"
Lance L. Littlejohn "The old meets the new: the Method of Frobenius and
Mathematica"
Peter A. McCoy "Orthogonal Polynomial and Special Function Methods in
Electromagnetics"
For information on the SIAM Annual Meeting see:
http://www.siam.org/meetings/an00/index.htm
Topic #4 ------------ OP-SF NET 7.2 ------------- March 15, 2000
~~~~~~~~~~~~~
From: Franek Szafraniec
Subject: Conference on Reproducing Kernel Hilbert Spaces
This conference was announced in OP-SF NET 7,1, Topic #4. It is to be held
in Krakow, April 16-21, 2000, to commemorate the 90th anniversary of
introducing the reproducing kernel property by Stanislaw Zaremba in two
papers published in 1907 and 1909. The conference web page is at:
http://www.im.uj.edu.pl/~fhszafra/
and the contact information is:
e-Mail: rkhs2000@im.uj.edu.pl
Regular mail:
RKHS2000 Conference
Instytut Matematyki UJ
ul. Reymonta 4
30-059 Krakow, Poland
fax:
+48 12 6324372
Topic #5 ------------ OP-SF NET 7.2 ------------- March 15, 2000
~~~~~~~~~~~~~
From: Centre for Mathematical Sciences
Subject: Summer School, Trivandrum: Special functions and functions of
matrix argument
DST - SPONSORED SECOND S.E.R.C SUMMER SCHOOL
ON
SPECIAL FUNCTIONS AND FUNCTIONS OF MATRIX ARGUMENT
(THEORY, APPLICATIONS, REAL AND COMPLEX CASES)
(29th MAY-30th JUNE 2000)
ORGANISED BY
CENTRE FOR MATHEMATICAL SCIENCES, TRIVANDRUM - 695581
Theory of special functions or transcendental functions of a real
scalar variable was originally developed for tackling problems in applied
mathematics, physics and engineering. For dealing with more advanced
problems in various disciplines it became necessary to develop the theory
of generalized hypergeometric functions, Meijer's G-function and Fox's
H-function, Appell, Lauricella and other functions. Then in the 1960's
and 1970's these generalized functions found applications in statistical
distribution theory, econometrics, psychometry, biometry, astrophysics
problems such as energy generation, stellar models, luminosity of stars,
etc. Special functions in complex variables found applications in many
areas especially in communication found applications in many areas
especially in communication problems, radar, tracking devices, signal
suppression and so on. Then it became necessary to develop special
functions of one or many matrix arguments.
The Centre for Mathematical Sciences (CMS) had organized a six weeks
summer school in 1995, sponsored by the Department of Science and
Technology, New Delhi. This was aimed at research workers, young faculty
and post-doctoral fellows who are interested in the theoretical
development, and applications of special functions in various disciplines.
Starting from the fundamentals, a number of topics such as classical
hypergeometric, basic hypergeometric and generalized hypergeometric
functions were brought to the current research level in that summer
school. The best research workers in India in this field gave the
lectures, followed by problem sessions by the local faculty. This was a
highly successful summer school and the proposed school will also bring a
number of topics from the fundamentals to the current research level,
along with applications in various disciplines.
Topics to be covered:
- Gamma, beta, psi, zeta functions
Bessel, Whittaker, hypergeometric functions
- Generalized hypergeometric, G and H-functions
- Introduction to basic hypergeometric functions
- Appell's and Lauricella functions
Jacobians of matrix transformations
and functions of matrix argument
- Current research topics and current
applications in statistics, econometrics,
physics and engineering
Faculty
Proposed visiting faculty
Dr. R. P. Agarwal (Lucknow)
Dr R. K. Saxena (Jodhpur)
Dr. H.L.Manocha (Delhi)
Dr. Srinivasa Rao (Chennai)
Dr. Thankavelu (Bangalore)
Dr.R.Jagannathan (Chennai)
Dr. A.M. Mathai (Canada)
Local faculty:
Dr.K.S. S.Nambooripad (Director in-charge, CMS)
Dr. R. N. Pillai (CMS)
Dr.T.S.K.Moothathu (CMS and Univ. of Kerala)
Dr. M.R. Kaimal (CMS and Univ. of Kerala)
Dr. M.I. Jinnah(CMS and Univ. of Kerala)
Dr. Yageen Thomas (CMS and Univ. of Kerala)
Dr. S. Radhakrishnan Chettiyar (CMS)
Dr. A.M.Mathai (Director, CMS)
Dr. A. Sukumaran Nair (Chairman, CMS)
The School, sponsored by the Department of Science and Technology,
Government of India is intended for the benefit of Ph.D students, young
post-doctoral fellows, young lecturers and fresh M.Sc's waiting to
register for a Ph.D programme. Preference will be given to graduates in
mathematics with proper exposure to probability and statistics, in
mathematical statistics, in theoretical physics with good background in
mathematics and some exposure to statistics. Financial support for train
travel, boarding and lodging will be provided to the participants.
Applications in plain paper (no application fee) should include mailing
address, date of birth, marital status, full academic record (send only
xerox copies, no originals), list of publications, research interest,
justification for participation, a letter from the Head of the Institution
indicating permission and leave to attend the school and a self addressed
empty envelope with Rs. 3/- stamp affixed (this is for acknowledging
receipt of application and mailing back further information) and the
completed application should reach the following address on or before 30th
March 2000.
DIRECTOR, CENTRE FOR MATHEMATICAL SCIENCES,
PANGAPPARA P.O., TRIVANDRUM 695 581
KERALA STATE, INDIA
PHONE: (0471) 415860
E-mail : cms@md3.vsnl.net.in, kssn@md2.vsnl.net.in
Topic #6 ------------ OP-SF NET 7.2 ------------- March 15, 2000
~~~~~~~~~~~~~
From: Renato Alvarez-Nodarse
Subject: Conference on Functional Analysis and Approximation Theory
The following information is form the WWW page:
http://www.dm.uniba.it/maratea/index.htm
The fourth edition of the "International Conference on Functional Analysis
and Approximation Theory" is organized in the sphere of activities of the
Center for Studies in Functional Analysis and Approximation Theory of the
University of Basilicata (Potenza), with the collaboration of the
Department of Mathematics of the University of Basilicata (Potenza), the
Department of Mathematics of the University and the Polytechnic of Bari.
Moreover it will be held under the auspices of the University of
Basilicata, the University of Bari, the Polytechnic of Bari, the National
Group of Functional Analysis and Applications (G.N.A.F.A.) and the
Progetti di Ricerca di Interesse Nazionale: Analisi Funzionale
(M.U.R.S.T.).
The organizing committee consists of Francesco Altomare (University of
Bari), Antonio Attalienti (University of Bari), Michele Campiti
(Polytechnic of Bari), Biancamaria Della Vecchia (University of Roma "La
Sapienza"), Giuseppe Mastroianni (University of Basilicata), Mario Rosario
Occorsio (University of Napoli).
The meeting will be devoted to some significant aspects of contemporary
mathematical research on Functional Analysis and Approximation Theory
including the applications of these fields in other areas.
Suggested topics include:
- Banach spaces, Banach lattices, function spaces.
- (Positive) linear operators, semigroups of (positive) linear operators,
evolution equations.
- Approximate quadratures and integral equations.
- Approximation methods in abstract spaces and in function spaces,
approximation by (positive) operators, interpolation, polynomial
approximation.
- Constructive approximation.
- Orthogonal polynomials.
The scientific program will consist of
invited survey talks (45 minutes) and
short communications (20 minutes).
The abstracts of all contributions and the program of the meeting will be
available at the beginning of the meeting. The list of invited speakers
and a preliminary list of all participants will be sent together with the
second announcement and will be published on this Web page as soon as
possible.
It is expected that the proceedings of the Conference will be published.
If you need to contact the Organizing Committee for any question or
request, please use the following E-Mail address: maratea@dm.uniba.it
Topic #7 ------------ OP-SF NET 7.2 ------------- March 15, 2000
~~~~~~~~~~~~~
From: Federico Pellarin
Subject: two questions on K_\nu
[from opsftalk]
Here are two questions I cannot solve:
(1) Let $K_{\nu}(z)$ the modified Bessel function of the third kind (following
the usual notations of the Bateman Manuscript Project). Fix $a$ a real number,
let $\nu=ia$ and consider the function \[f(t)=K_{\nu}(e^{-2\pi t}).\]
I wish to prove, at least for $t$ very big, that $f(t)$
approaches a periodic function of period $1/a$, that I should
study in the sequel.
A similar sub-question arise with the function
\[g(t)=K_{it}(z)e^{\pi t/2},\]
for $z>0$ fixed and $t$ big enough.
Of course, I don't know whether my hypotheses are reasonable, it's also
possible that I'm completely wrong. Is there anyone knowing the answer?
(2) I found p. 96 of the book "Higher Transcendental Functions" Vol. 2 a
formula (the formula (60) of Nicholson) expressing the product of two
Bessel functions of third kind $K_{\mu}(Z)K_{\nu}(z)$ as an infinite
integral involving $K_{\mu+\nu}$ "along the real axis".
The question, very naive, is: are there some "similar" formulas for
products of three or more functions such as $K_{\mu}(Z)K_{\nu}(z)
K_{\eta}(\zeta)\ldots $ or at least for $K_{\mu}(z)K_{\nu}(z)
K_{\eta}(z)\ldots $? This formula should not be an "avatar" of the usual
addition theorem. In particular, I'm only considering integrals of one
variable.
Did anyone investigate successfully such a kind of question?
Thank you very much,
Federico Pellarin
Topic #8 ------------ OP-SF NET 7.2 ------------- March 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: New Indian Society for Special Functions and Their Applications
A new Indian Society for Special Functions and Their Applications has been
formed with a web site maintained by Professor K. Srinivasa Rao
at
http://www.imsc.ernet.in/~ssfa/
The Society has concluded an agreement with our Activity Group concerning
mutual cooperation and exchange of Newsletter material.
Topic #9 ------------ OP-SF NET 7.2 ------------- March 15, 2000
~~~~~~~~~~~~~
From: Lothar Reichel
Subject: Proceedings - Madrid Workshop on Orthogonal Polynomials
The Electronic Transactions on Numerical Analysis (ETNA), Vol. 9, 1999
contains the Proceedings of the International Workshop on Orthogonal
Polynomials held at University Carlos III de Madrid in Leganes, Spain,
1998, organized by M. Alfaro, R. Alvarez-Nodarse, J. Arvesz and F.
Marcellan (Chair). The proceedings were edited by R. Alvarez-Nodarse and
F. Marcellan.
The Electronic Transactions on Numerical Analysis (ETNA), can be accessed
at the web site: http://rattler.cameron.edu/EMIS/journals/ETNA/index.html
Table of contents:
M. Alvarez de Morales, T. E. Pirez, M. A. Piqar and A. Ronveaux,
Non-standard orthogonality for Meixner polynomials.
G. S. Ammar, D. Calvetti and L. Reichel,
Computation of Gauss-Kronrod quadrature rules with non-positive weights.
F. Cala Rodriguez, P. Gonzalez-Vera, and M. Jimenez Paiz,
Quadrature formulas for rational functions.
C. Costa and R. Serodio,
A footnote on quaternion block-tridiagonal systems.
E. M. Garcia-Caballero, T. E. Pirez and M. A. Piqar,
Sobolev orthogonal polynomials: interpolation and approximation.
W. Gautschi,
Orthogonal polynomials and quadrature.
W. Koepf,
Software for the algorithmic work with orthogonal polynomials and
special functions.
M. Lorente,
Creation and annihilation operators for orthogonal polynomials of
continuous and discrete variables.
F. Marcellan and J. C. Medem,
q-Classical orthogonal polynomials: a very classical approach.
P. Natalini, S. Noschese and P. E. Ricci,
An iterative method for computing the eigenvalues of second kind
Fredholm operators and applications.
J. Segura and A. Gil,
Evaluation of associated Legendre functions off the cut and parabolic
cylinder functions.
Doron Zeilberger,
Proof of a conjecture of Chan, Robbins, and Yuen.
Topic #10 ------------ OP-SF NET 7.2 ------------- March 15, 2000
~~~~~~~~~~~~~
From: Axel Riese
Subject: SIAM Outreach Membership
The SIAM Board of Trustees has approved a proposal to provide an
affordable membership option for individuals who live and work in
developing countries (as identified by the World Bank). This new
category of membership, called "outreach membership," was created to
help make SIAM products and services accessible to a wider and more
global group of applied and computational mathematicians. This is a
great alternative for individuals in developing countries who cannot
afford the full SIAM dues. For just $25 per year, eligible individuals
receive a slightly reduced set of benefits.
Outreach Members receive all print issues of SIAM News and
electronic-only access to SIAM Review. They can join any of the SIAM
Activity Groups at $10 per group, are entitled to 20% off list prices
on all SIAM books, and receive member discounted registration at SIAM
sponsored meetings. No additional journal subscriptions at membership
rates are available as part of the Outreach Membership.
The Outreach Membership application (secure) form can be found at
https://www.siam.org/membership/outreachmem.htm.
The list of developing countries (as identified by the World Bank) can
be found at http://www.siam.org/membership/outreachlist.htm.
SIAM
Society for Industrial and Applied Mathematics 3600 University City
Science Center
Philadelphia, PA 19104 USA
215-382-9800
fax 215-386-7999
siam@siam.org
www.siam.org
[Editor's Note: An article on this initiative, "SIAM Reaches Out to
Applied Mathematicians In Developing Countries" by SIAM President Gilbert
Strang appears in SIAM News, Volume 33, Number 1 January/February 2000.
See: http://www.siam.org/siamnews/01-00/reach.htm]
Topic #12 ------------ OP-SF NET 7.2 ------------- March 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
E-print math.CO/0001082
Title: Une identite remarquable en theorie des partitions
Authors: Alain Lascoux, Michel Lassalle (CNRS,Paris)
Categories: CO Combinatorics
Comments: 16 pages, LaTeX, in French
Abstract: We prove an identity about partitions, previously conjectured in
the study of shifted Jack polynomials (math.CO/9903020). The proof given
is using $\lambda$-ring techniques. It would be interesting to obtain a
bijective proof.
From: Lassalle
Date: Fri 14 Jan 2000
E-print math.CO/0001078
Title: A Probabilistic Proof of the Rogers Ramanujan Identities
Author: Jason Fulman
Categories: CO Combinatorics (CT Category Theory; NT Number Theory)
Abstract: The asymptotic probability theory of conjugacy classes of the
finite general linear and unitary groups leads to a probability measure on
the set of all partitions of natural numbers. A simple method of
understanding these measures in terms of Markov chains is given and
compared with work on the uniform measure. Elementary probabilistic proofs
of the Rogers-Ramanujan identities follow. As a corollary, the main case
of Bailey's lemma is interpreted as finding eigenvectors of the transition
matrix of the Markov chain. It is shown that the viewpoint of Markov
chains extends to quivers.
From: Jason Fulman
Revised: Mon 7 Feb 2000 21:24:15 GMT
E-print math.QA/0001114
Title: Fermionic formulas for level-restricted generalized Kostka
polynomials and coset branching functions
Authors: Anne Schilling, Mark Shimozono
Categories: QA Quantum Algebra (CO Combinatorics)
Math Subject Class: 05A19; 05A15; 17B65; 17B37; 81R50; 82B23
Comments: 67 pages, axodraw style file needed
Abstract: Level-restricted paths play an important role in crystal theory.
They correspond to certain highest weight vectors of modules of quantum
affine algebras. We show that the recently established bijection between
Littlewood--Richardson tableaux and rigged configurations is well-behaved
with respect to level-restriction and give an explicit characterization of
level-restricted rigged configurations. As a consequence a new general
fermionic formula for the level-restricted generalized Kostka polynomial
is obtained. Some coset branching functions of type $A$ are computed by
taking limits of these fermionic formulas.
From: Anne Schilling
Date: Thu 20 Jan 2000 20:42:10 GMT
E-print math.QA/0001006
Title: Summation and transformation formulas for elliptic hypergeometric
series
Author: S. O. Warnaar
Categories: QA Quantum Algebra (CO Combinatorics)
Math Subject Class: Primary 33D15, 33D67, 33E05; Secondary 05A30
Report number: ITF-99-42
Comments: 21 pages, AMS-LaTeX
Abstract: Using matrix inversion and determinant evaluation techniques we
prove several summation and transformation formulas for terminating,
balanced, very-well-poised, elliptic hypergeometric series.
From: S. Ole Warnaar
Date: Mon 3 Jan 2000 10:11:38 GMT
E-print math.QA/0002090
Title: Koornwinder polynomials and affine Hecke algebras
Author: J. V. Stokman
Categories: QA Quantum Algebra (RT Representation Theory)
Math Subject Class: 33D52; 33D80
Comments: 30 pages
Abstract: In this paper we derive the bi-orthogonality relations, diagonal
term evaluations and evaluation formulas for the non-symmetric Koornwinder
polynomials. For the derivation we use certain representations of the
(double) affine Hecke algebra which were originally defined by Noumi and
Sahi. We furthermore give the explicit connection between the
non-symmetric and the symmetric theory. This leads in particular to new
proofs of the orthogonality relations, quadratic norm evaluations and
evaluation formulas for the symmetric Koornwinder polynomials.
From: Jasper V. Stokman
Date: Fri 11 Feb 2000
E-print math.QA/0001184
Title: Differential Equations Compatible with KZ Equations
Authors: G. Felder, Y. Markov, V. Tarasov, A. Varchenko
Categories: QA Quantum Algebra
Math Subject Class: 35Q40; 17B10; 17B56; 81R10; 33C80
Comments: 34 pages, LaTeX
Abstract: We define a system of "dynamical" differential equations
compatible with the KZ differential equations. The KZ differential
equations are associated to a complex simple Lie algebra $\mathbf{g}$.
These are equations on a function of $n$ complex variables $z_i$ taking
values in the tensor product of $n$ finite dimensional
$\mathbf{g}$-modules. The KZ equations depend on the "dual" variable in
the Cartan subalgebra of $\mathbf{g}$. The dynamical differential
equations are differential equations with respect to the dual variable. We
prove that the standard hypergeometric solutions of the KZ equations also
satisfy the dynamical equations. As an application we give a new
determinant formula for the coordinates of a basis of hypergeometric
solutions.
From: Yavor Markov
Date: Mon 31 Jan 2000 23:54:48 GMT
Nonlinear Sciences, abstract nlin.SI/0001001
From: Dmitri Scherbin
Date (v1): Thu, 6 Jan 2000 22:32:36 GMT (16kb)
Date (revised v2): Tue, 18 Jan 2000 10:18:56 GMT (16kb)
Fermionic representation for basic hypergeometric functions related to
Schur polynomials
Authors: A.Yu.Orlov, D.M.Scherbin
Comments: 17 pages,LaTeX, no figures, misprints are corrected
Subj-class: Exactly Solvable and Integrable Systems
We present the fermionic representation for the q-deformed hypergeometric
functions related to Schur polynomials. For q=1 it is known that these
hypergeometric functions are related to zonal spherical polynomials for
GL(N,C)/U(N) symmetric space. Multivariate hypergeometric functions appear
to be tau-functions of the KP and of the two-dimensional Toda lattice
hierarchies. The variables of the hypergeometric functions are the higher
times of those hierarchies. The discrete Toda lattice variable shifts
parameters of hypergeometric functions.
Astrophysics, abstract astro-ph/0001279
From: "Hans J. Haubold"
Date: Sun, 16 Jan 2000 10:03:59 GMT (9kb)
The Fractional Kinetic Equation and Thermonuclear Functions
Authors: H.J. Haubold (UN, Austria), A.M. Mathai (McGill University, Canada)
Comments: 14 pages, LaTeX
The paper discusses the solution of a simple kinetic equation of the type
used for the computation of the change of the chemical composition in
stars like the Sun. Starting from the standard form of the kinetic
equation it is generalized to a fractional kinetic equation and its
solutions in terms of H-functions are obtained. The role of thermonuclear
functions, which are also represented in terms of G- and H-functions, in
such a fractional kinetic equation is emphasized. Results contained in
this paper are related to recent investigations of possible astrophysical
solutions of the solar neutrino problem.
Astrophysics, abstract astro-ph/0001280
From: "Hans J. Haubold"
Date: Sun, 16 Jan 2000 10:13:52 GMT (7kb)
Analytical Study of Thermonuclear Reaction Probability Integrals
Authors: M.A. Chaudhry (King Fahd University, Saudi Arabia), H.J. Haubold
(UN, Austria), A.M. Mathai(McGill University, Canada)
Comments: 12 pages, LaTeX
An analytic study of the reaction probability integrals corresponding to
the various forms of the slowly varying cross-section factor $S(E)$ is
attempted. Exact expressions for reaction probability integrals are
expressed in terms of the extended gamma functions.
E-print math.CA/0002226
Title: Orthogonal Polynomials and Generalized Oscillator Algebras
Author: V. V. Borzov (U. of Telecommunications, St.Petersburg)
Categories: CA Classical Analysis (QA Quantum Algebra)
Math Subject Class: 33C45, 33C80, 33D45, 33D80
Comments: 23 pages, no figures, submitted to Integral Transforms and Special
Functions
Abstract: For any orthogonal polynomials system on real line we construct an
appropriate oscillator algebra such that the polynomials make up the
eigenfunctions system of the oscillator hamiltonian. The general scheme is
divided into two types: a symmetric scheme and a non-symmetric scheme. The
general approach is illustrated by the examples of the classical orthogonal
polynomials: Hermite, Jacobi and Laguerre polynomials. For these polynomials we
obtain the explicit form of the hamiltonians, the energy levels and the
explicit form of the impulse operators.
From: "E.V. Damaskinsky"
Date: Sat 26 Feb 2000 21:04:09 GMT
E-print math.CO/9912093
Title: Riemann-Hilbert problem and the discrete Bessel kernel
Author: Alexei Borodin
Categories: CO Combinatorics (MP Mathematical Physics)
Comments: AMSTeX, 23 pages. Formalism of general discrete integrable operators
has been added
Abstract: We use discrete analogs of Riemann-Hilbert problem's methods
to derive the discrete Bessel kernel which describes the poissonized
Plancherel measures for symmetric groups. To do this we define
discrete analogs of a Riemann-Hilbert problem and of an integrable
integral operator and show that computing the resolvent of a discrete
integrable operator can be reduced to solving a corresponding discrete
Riemann-Hilbert problem.
We also give an example, explicitly solvable in terms of classical
special functions, when a discrete Riemann-Hilbert problem converges in a
certain scaling limit to a conventional one; the example originates from
the representation theory of the infinite symmetric group.
From: Alexei Borodin
Date: Sun 12 Dec 1999 17:46:39 GMT
Revised: Thu 9 Mar 2000 18:19:21 GMT
Topic #13 ------------ OP-SF NET 7.2 ------------- March 15, 2000
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From: OP-SF NET Editor
Subject: Changes of Address, WWW Pages, etc
Victor Adamchik asks that we update the link to his home page. The new one
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