## OP-SF WEB

### Extract from OP-SF NET

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,
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

With kind regards,

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 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
- 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: 33F10 Symbolic computation (Zeilberger algorithm, etc.)

- 34B30, change into:
Special equations (Mathieu, Hill, Bessel, Painlev\'e, etc.)

- add: 40A27 Explicit summation of series
- add: 40A29 Explicit computation of integrals
- add: 40B10 Rearrangements of explicit multiple series
- add: 40B15 Multiple integrals (should also be assigned at least one
other classification number in this section)

- 42C05, change into: Orthogonal functions and polynomials in one
- add: 42C07 Orthogonal functions and polynomials in several variables,
- add: 42C45 Biorthogonal families of functions