OP-SF NET 4-4 --------- July 15, 1997 From: Tom Koornwinder thk@wins.uva.nl To: Prof. Keith Dennis (Executive Editor Mathematical Reviews) Prof. Bernd Wegner (Chefredakteur Zentralblatt fuer Mathematik) Dear Editors, In reply to your call for comments and suggestions for the revision of the Mathematics Subject Classification I send you here a large number of suggestions from the community of Orthogonal Polynomials and Special Functions. The SIAM Activity Group on Orthogonal Polynomials and Special Functions has solicited reactions via the elctronic Newsletter OP-SF Net (freely available for all interested people) and the printed Newsletter of the Activity Group (only for members). On the basis of the reactions we received I have made a comprehensive proposal for changes of those parts of the 1991 Classification which deal with Orthogonal Plynomials and Special Functions (in particular part 33). A preliminary version of this final proposal I recently discussed with prof. Richard Askey, and he agreed with it. Experts from our Activity Group are available if you need further feed-back in the area of Orthogonal Polynomials and Special Functions during your revision process. With kind regards, Tom Koornwinder about 33 - 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 Orthogonal polynomials and 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 - add: 33C67 Hypergeometric functions associated with root systems - 33C80, change into: Connections with groups, algebras and related topics - 33D10: skip this Motivation: we know theta functions but we do not know basic theta functions - 33D15, change into: Basic hypergeometric functions in one variable, ${}_r\phi_s$ - 33D20: skip this Motivation: studying ${}_2\phi_1$ immediately gives rise to studying more general ${}_r\phi_s$ - 33D45, change into: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) - add: 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable - add: 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) - 33D55: skip this Motivation: Basic spherical functions in the sense of spherical functions on quantum groups are covered by 33D80. If basic spherical harmonics mean the elements in irreducible subspaces of the algebra of polynomials on a quantum sphere then these are also covered by 33D80. - add: 33D67 Basic hypergeometric functions associated with root systems - 33D80, change into: Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras and related topics - add: 33E12 Mittag-Leffler functions and generaliztions - add: 33Fxx Computational aspects - add: 33F05 Numerical approximation [See also 65D20] - add: 33F10 Symbolic computation (Zeilberger algorithm, etc.) [See also 68Q40] about 34 - 34B30, change into: Special equations (Mathieu, Hill, Bessel, Painlev\'e, etc.) about 40 - add: 40A27 Explicit summation of series - add: 40A29 Explicit computation of integrals - add: 40A40 Generating functions [See also 05A15] - add: 40B10 Rearrangements of explicit multiple series - add: 40B15 Multiple integrals (should also be assigned at least one other classification number in this section) about 42 - 42C05, change into: Orthogonal functions and polynomials in one variable, general theory [See also 33C45, 33C47, 33D45] - add: 42C07 Orthogonal functions and polynomials in several variables, general theory [See also 33C50, 33C52, 33D50, 33D52] - add: 42C40 Wavelets - add: 42C45 Biorthogonal families of functions about 65 - 65D20, change into: Computation of special functions, construction of tables [See also 33F05] about 68 - 68Q40, add to "See also" a ref to 33F10 (warning: 68Q40 gives a ref to 16-08, but 16-08 does not exist)

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