| 33-XX |
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Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics, see 05Axx; for number-theoretic aspects, see 11-XX; for representation theory, see 22Exx} |
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33-00 |
General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions |
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33-01 |
Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions |
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33-02 |
Research exposition (monographs, survey articles) pertaining to special functions |
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33-03 |
History of special functions [Consider also classification numbers from Section 01-XX] |
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33-04 |
Software, source code, etc. for problems pertaining to special functions |
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33-06 |
Proceedings, conferences, collections, etc. pertaining to special functions |
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33-11 |
Research data for problems pertaining to special functions |
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33B10 |
Exponential and trigonometric functions |
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33B15 |
Gamma, beta and polygamma functions |
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33B20 |
Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) |
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33B30 |
Higher logarithm functions |
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33B99 |
None of the above, but in this section |
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33C05 |
Classical hypergeometric functions, ${}_2F_1$ |
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33C10 |
Bessel and Airy functions, cylinder functions, ${}_0F_1$ |
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33C15 |
Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$ |
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33C20 |
Generalized hypergeometric series, ${}_pF_q$ |
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33C45 |
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) {For general orthogonal polynomials and functions, see also 42C05} |
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33C47 |
Other special orthogonal polynomials and functions |
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33C50 |
Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable |
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33C52 |
Orthogonal polynomials and functions associated with root systems |
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33C55 |
Spherical harmonics |
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33C60 |
Hypergeometric integrals and functions defined by them ($E$, $G$, $H$ and $I$ functions) |
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33C65 |
Appell, Horn and Lauricella functions |
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33C67 |
Hypergeometric functions associated with root systems |
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33C70 |
Other hypergeometric functions and integrals in several variables |
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33C75 |
Elliptic integrals as hypergeometric functions |
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33C80 |
Connections of hypergeometric functions with groups and algebras, and related topics |
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33C90 |
Applications of hypergeometric functions |
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33C99 |
None of the above, but in this section |
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33D05 |
$q$-gamma functions, $q$-beta functions and integrals |
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33D15 |
Basic hypergeometric functions in one variable, ${}_r\phi_s$ |
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33D45 |
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) |
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33D50 |
Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable |
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33D52 |
Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) |
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33D60 |
Basic hypergeometric integrals and functions defined by them |
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33D65 |
Bibasic functions and multiple bases |
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33D67 |
Basic hypergeometric functions associated with root systems |
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33D70 |
Other basic hypergeometric functions and integrals in several variables |
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33D80 |
Connections of basic hypergeometric functions with quantum groups, Chevalley groups, $p$-adic groups, Hecke algebras, and related topics |
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33D90 |
Applications of basic hypergeometric functions |
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33D99 |
None of the above, but in this section |
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33E05 |
Elliptic functions and integrals |
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33E10 |
Lamé, Mathieu, and spheroidal wave functions |
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33E12 |
Mittag-Leffler functions and generalizations |
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33E15 |
Other wave functions |
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33E17 |
Painlevé-type functions |
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33E20 |
Other functions defined by series and integrals |
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33E30 |
Other functions coming from differential, difference and integral equations |
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33E50 |
Special functions in characteristic $p$ (gamma functions, etc.) |
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33E99 |
None of the above, but in this section |
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33F05 |
Numerical approximation and evaluation of special functions [See also 65D20] |
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33F10 |
Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) [See also 68W30] |
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33F99 |
None of the above, but in this section |
