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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}
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|
33-00
|
General reference works (handbooks, dictionaries, bibliographies, etc.)
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|
33-01
|
Instructional exposition (textbooks, tutorial papers, etc.)
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33-02
|
Research exposition (monographs, survey articles)
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|
33-03
|
Historical {!must also be assigned at least one classification number from section 01}
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|
33-04
|
Explicit machine computation and programs (not the theory of computation or programming)
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|
33-06
|
Proceedings, conferences, collections, etc.
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|
33Bxx
|
Elementary classical 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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|
33Cxx
|
Hypergeometric functions
|
|
33C05
|
Classical hypergeometric functions, 2F1
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|
33C10
|
Bessel and Airy functions, cylinder functions, 0F1
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|
33C15
|
Confluent hypergeometric functions, Whittaker functions, 1F1
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|
33C20
|
Generalized hypergeometric series, pFq
|
|
33C45
|
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
{For general orthogonal polynomials and functions, see
42C05}
|
|
33C47
|
Other special orthogonal polynomials and functions
|
|
33C50
|
Orthogonal polynomials and functions in several variables expressible in terms of special functions in one varaible
|
|
33C52
|
Orthogonal polynomials and functions associated with root systems
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|
33C55
|
Spherical harmonics
|
|
33C60
|
Hypergeometric integrals and functions defined by them (E, G and H functions)
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|
33C65
|
Appell, Horn and Lauricella functions
|
|
33C67
|
Hypergeometric functions associated with root systems
|
|
33C70
|
Other hypergeometric functions and integrals in several variables
|
|
33C75
|
Elliptic integrals as hypergeometric functions
|
|
33C80
|
Connections with groups, algebras, 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
|
|
33D15
|
Basic hypergeometric functions in one variable, r\phis
|
|
33D45
|
Basic orthogonal polynomials and functions (Askey - Wilson polynomials, etc.)
|
|
33D50
|
Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable
|
|
33D52
|
Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
|
|
33D60
|
Basic hypergeometric integrals and functions defined by them
|
|
33D65
|
Bibasic functions and multiple bases
|
|
33D67
|
Basic hypergeometric functions associated with root systems
|
|
33D70
|
Other basic hypergeometric functions and integrals in several variables
|
|
33D80
|
Connections with quantum groups, Chevalley groups, p-adic groups, Hecke 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
|
Lam\'e, Mathieu, and spheroidal wave functions
|
|
33E12
|
Mittag-Leffler functions and generalizations
|
|
33E15
|
Other wave functions
|
|
33E17
|
Painlev\'e-type functions
|
|
33E20
|
Other functions defined by series and integrals
|
|
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
|
|
33Fxx
|
Computational aspects
|
|
33F05
|
Numerical approximation
[See also
65D20]
|
|
33F10
|
Symbolic computation (Gosper and Zeilberger algorithms, etc.)
[See also
68W30]
|
|
33F99
|
None of the above, but in this section
|