Topic #22 ------------- OP-SF NET -------------- November 15, 1996 ~~~~~~~~~ From: OP-SF Net editor Subject: Part 33 of 1991 Mathematics Subject Classification Classification: 33-XX Special functions, {33-XX deals with the properties of functions as functions. For orthogonal functions, See also 42Cxx; for aspects of combinatorics, See 05Axx; for number-theoretic aspects, See 11-XX; for representation theory, See 22Exx} 33-00 General reference works (handbooks, dictionaries, bibliographies, etc.) 33-01 Instructional exposition (textbooks, tutorial papers, etc.) 33-02 Research exposition (monographs, survey articles) 33-03 Historical (must be assigned at least one classification number from Section 01) 33-04 Explicit machine computation and programs (not the theory of computation or programming) 33-06 Proceedings, conferences, collections, etc. 33Bxx Elementary classical functions 33B10 Exponential and trigonometric functions 33B15 Gamma, beta and polygamma functions 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) 33B99 None of the above but in this section 33Cxx Hypergeometric functions 33C05 Classical hypergeometric functions, $_2F_1$ 33C10 Bessel and Airy functions, cylinder functions, $_0F_1$ 33C15 Confluent hypergeometric functions, Whittaker functions, $_1F_1$ 33C20 Generalized hypergeometric series, $_pF_q$ 33C45 Orthogonal polynomials and functions (Chebyshev, Legendre, Gegenbauer, Jacobi, Laguerre, Hermite, Hahn, etc.) 33C50 Orthogonal polynomials and functions in several variables 33C55 Spherical functions, spherical harmonics, ultraspherical polynomials 33C60 Hypergeometric integrals and functions defined by them ($E$, $G$ and ${H}$ functions) 33C65 Appell, Horn and Lauricella functions 33C70 Other hypergeometric functions and integrals in several variables 33C75 Elliptic integrals as hypergeometric functions 33C80 Connections with groups, algebras, root systems and related topics 33C90 Applications 33C99 None of the above but in this section 33Dxx Basic hypergeometric functions 33D05 $q$-gamma functions, $q$-beta functions and integrals 33D10 Basic theta functions 33D15 Basic hypergeometric functions in one variable 33D20 Generalized basic hypergeometric series 33D45 Basic orthogonal polynomials and functions in one and several variables 33D55 Basic spherical functions, spherical harmonics (continuous and discrete) 33D60 Basic hypergeometric integrals and functions defined by them 33D65 Bibasic functions and multiple bases 33D70 Other basic hypergeometric functions and integrals in several variables 33D80 Connections with groups, algebras, and related topics 33D90 Applications 33D99 None of the above but in this section 33Exx Other special functions 33E05 Elliptic functions and integrals 33E10 Lame, Mathieu, and spheroidal wave functions 33E15 Other wave functions 33E20 Other functions defined by series and integrals 33E30 Other functions coming from differential, difference and integral equations 33E99 None of the above but in this section

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