SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #5 -------------- OP-SF NET 4.2 ------------- March 15,1997

From: Tom Koornwinder (, Walter Van Assche (

Subject: Report from Madras Workshop on Special Functions & Differential Equations: Chennai (Madras), India, January 13-24, 1997

A workshop on special functions and differential equations was held at the "Institute of Mathematical Sciences" in Chennai (formerly known as Madras) in India, from January 13 to January 24, 1997. The main organizer was K. Srinivasa Rao, who succeeded in getting about 75 participants, with approximately two thirds of them from India. The other participants were from Belgium (7), The Netherlands (3), Australia (2), New Zealand, Finland, Canada, Poland, Germany, Austria, France, and Italy (each 1), and some people from India working temporarily abroad.

The background of speakers and participants was partly from pure and applied mathematics and partly from mathematical and theoretical physics. At least half of the lectures dealt with the first conference theme, special functions. The other theme of differential equations was approached both from the analytic side and from the numerical side. A few lectures merged both themes. All lectures were plenary and invited and had a standard length of 45 minutes. There were quite a few minicourses consisting of two or three lectures. The topics of these minicourses ranged over: Ramanujan's mock theta functions; connection and linearization coefficients for orthogonal polynomials; generalizations of Laguerre polynomials by adding (a derivative of) delta(x) to the weight function; applications of 3j, 6j and 9j coefficients to special function theory; irrationality and transcendence proofs of some famous numbers by approximation theory; special functions associated with root systems; creation operators for Jack and Macdonald polynomials; numerical methods for solving o.d.e.'s; parallel algorithms for solving o.d.e.'s; non-linear quantum mechanics; the uncertainty principle; nonlinear evolution equations. D.-N. Verma (of Verma module fame) gave some informal seminars on Lie theory, Clebsch-Gordan coefficients and related matters, and Tom Koornwinder filled a gap in the program by giving a seminar lecture on Zeilberger's algorithm.

The workshop even made the local newspaper and television due to a special lecture "A nuclear-weapon free world: desirable? possible? probable?" by F. Calogero, secretary general of the Pugwash conferences on science and world affairs, which was attended by his excellency R. Venkataraman, former president of India.

During the opening ceremony of the workshop, R.P. Agarwal gave a survey on special functions in India during the last century. Among others, the theory of q-special functions, the (Miller type) Lie theoretic approach to special functions, and applications to theoretical physics and probability theory are well represented nowadays in India. Professor Agarwal concluded his survey with a call to avoid superficial work and to look always for deep results. Tom Koornwinder, as vice-chair of our SIAM Activity Group, was asked to make some remarks in reply. He indicated some further active research areas in our field, such as special functions of several variables, their relation with certain algebraic structures (Lie groups and algebras, root systems, quantum groups, Hecke algebras), the general theory of orthogonal polynomials (including the Sobolev inner products), computer algebra methods for finding hypergeometric identities, and the application of special functions in real life situations (engineering). Some of these aspects indeed were the subject of subsequent lectures.

During the workshop there was an informal meeting for founding a Society for Special Functions & Applications in India. Its aim will be to promote research in this area, to inform people of what is going on, and possibly to create a new India-based forum for bringing out research publications of international standard on special functions. Application forms for life-long membership are already available. Interaction with our SIAM activity group looked desirable to all present at the discussions, certainly concerning the Newsletter.

A very extensive cultural program was prepared by the organizers. Among the events were a dance performance, a concert of traditional Indian music, a trip to a drive-in movie to see a Tamil version of Mrs. Doubtfire, and on Sunday a visit to the temple cities Kancheepuram and Mahabalipuram for visiting the temples (barefoot of course) and to do business with the local sandal makers and sculptors (bargaining skill is desirable).

Ramanujan is of course very closely connected with Chennai and a visit to the Ramanujan museum and the Ramanujan Institute for Mathematical Sciences of the University of Madras was therefore a natural part of the program. The Ramanujan museum is a rather recent realisation located in a mathematics education center. Srinivasa Rao gave a lecture on the life and work of Ramanujan and afterwards we were able to see the displays in the museum. Some of Ramanujan's work is very suitable for use in mathematics courses at all levels and the Ramanujan museum wants to advertize this idea. Our visit to the museum ended with a delicious high tea organized with great care and effort by the mathematics education center.

All western participants were impressed by the quality of the hosting Institute of Mathematical Sciences, the great hospitality, and (for newcomers) the fascinating intricacies of Indian culture and society. The efforts of prof. K. Srinivasa Rao to make this workshop into a success are really beyond praise.

Tom H Koornwinder
Walter Van Assche

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