Topic #3 --------------- OP-SF NET -------------- November 15, 1996 ~~~~~~~~~ From: Tom Koornwinder email@example.com Subject: Revising the 1991 Mathematics Subject Classification In OP-SF Net 3.3, topic #12, we printed information which was taken from Notices AMS, December 1995, p.1547, see also WWW: http://www.ams.org/committee/publications/msc-2000-let.html. We called then for suggestions for revision concerning the sections on Orthogonal Polynomials and Special Functions. (For your convenience we have included part 33 of the 1991 Math. Subject Classification here) Up to now we have received the following comments: Wolfram Koepf : - In one way or the other the Askey-Wilson scheme should appear here. One could mention these in 33C45 and 33D45. A distinction between these "classical" systems and other systems could also be helpful. - Algorithmic methods, and/or the use of symbolic computation could be mentioned explicitly. Charles Dunkl : - Should wavelets get more attention in 42c? - A finer classification of Askey-Wilson types? - A cross-reference to quantum groups? Tom Koornwinder : - 33C45, change into: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.; see 42C05 for general orthogonal polynomials and functions) - add: 33C47 Other special orthogonal polynomials and functions - 33C50: change into: Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable - add: 33C52 Special functions associated with root systems - 33C55, change into: Spherical harmonics Motivation: ultraspherical polynomials unrelated to spherical harmonics are covered by 33C45; spherical functions (on Gelfand pairs) are covered by 33C80 - 33C80, change into: Connections with groups, algebras and related topics - 33D10: What is the difference between theta functions and basic theta functions? - 33D15 and 33D20: What is the distinction between basic hypergeometric functions and generalized hypergeometric functions? For instance: the first category is r phi s with r<=2 and s<=1 and the second category is general r phi s ? - 33D45, change into: Orthogonal polynomials and functions of q-hypergeometric type (Askey-Wilson polynomials, etc.) - add: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of q-special functions in one variable - add: 33D52 q-Special functions associated with root systems - 33D55: skip this item, it is not clear what is meant. - 33C80, change into: Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras and related topics - 42C05. change into: Orthogonal functions and polynomials in one variable, general theory [See also ... ] - add: 42C07: Orthogonal functions and polynomials in several variables, general theory [See also ... ] Readers of OP-SF Net are invited to send us their comments for inclusion in the next (January 1997) issue of OP-SF Net. All comments will be eventually bundled and passed to the Executive Editor of Mathematical Reviews.