o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o 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 o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o 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 ~~~~~~~~~~~~~ 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 is http://www.acs.ilstu.edu/faculty/adamchik/ Also, the link to his "Integral and series representations for Catalan's constant" is http://www.acs.ilstu.edu/faculty/adamchik/articles/catalan.htm Topic #14 ------------ OP-SF NET 7.2 ------------- March 15, 2000 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: Subscribing to OP-SF NET There are two ways to subscribe to OP-SF NET: 1. Send a message to poly-request@siam.org with your name and email address in the body of the message. If everything works well, you will be put on the mailing list of OP-SF NET which is maintained by SIAM. 2. Send a message to listproc@nist.gov and put in the body of the message the single line: subscribe opsfnet xxxxx where in place of xxxxx you put your name. This is handled by an automatic list server. You will receive a confirmation, with a list of further commands. You will be put on the opsfnet mailing list of this list server. A new issue of OP-SF NET will be mailed to people on this list immediately after the mailing by SIAM to the people on SIAM's list. To cancel your subscription, send "unsubscribe opsfnet" to the same address. In case of any trouble with mailings of OP-SF Net, send a message to dlozier@nist.gov. Topic #15 ------------ OP-SF NET 7.2 ------------- March 15, 2000 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: Obtaining back issues of OP-SF NET and submitting contributions to OP-SF NET and Newsletter Back issues of OP-SF NET can be obtained from WWW: http://turing.wins.uva.nl/~thk/opsfnet/ or WWW: http://www.math.ohio-state.edu/JAT/DATA/OPSFNET/opsfnet.html Contributions to the OP-SF NET 7.3 should reach the email address poly@siam.org before May 1, 2000. The Activity Group also sponsors a (printed) Newsletter edited by Renato Alvarez-Nodarse and Rafael Yanez. The deadline for submissions to be included in the June 2000 issue is May 15, 2000 and for the October 2000 issue it is September 15, 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. Please note that submissions to the Newsletter (if not containing mathematics symbols or pictures) are automatically considered for publication in OP-SF NET, and vice versa, unless the writer requests otherwise. Previous issues of the Newsletter, but not the most recent one, can be obtained as dvi or PostScript files from Wolfram Koepf's WWW homepage: http://www.imn.htwk-leipzig.de/~koepf/siam.html In order to join the SIAM Activity Group on Orthogonal Polynomials and Special Functions, and thereby receive the Newsletter, you have to become a member of SIAM. The annual dues are $99 for SIAM plus $10 for the Group. Student memberships are $20 a year with free membership in one Activity Group. Postgraduates can join for $45 a year (for three years). There is special rate of $25 per year for applied mathematicians from developing countries. Contact the email address join@siam.org o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o 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. o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o 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: http://math.nist.gov/opsf/ Information on joining SIAM and this activity group: service@siam.org o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o 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 o - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o