| 33-XX | | Prev: 32 | Up: Top | Next: 34 | |
| 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} |
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 also 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)
| 33B30 |
Higher logarithm functions
| 33B99 |
None of the above, but in this section
| |
33Cxx
| Hypergeometric functions
[xref: 05A10, 05A15]
| 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 of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See 42C05 for general orthogonal polynomials and functions]
[xref: 05E35, 42C05]
| 33C47 |
Other special orthogonal polynomials and functions
| 33C50 |
Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
[xref: 05E35, 42C05]
| 33C52 |
Orthogonal polynomials and functions associated with root systems
| 33C55 |
Spherical harmonics
| 33C60 |
Hypergeometric integrals and functions defined by them ($E$, $G$ and ${H}$ functions)
| 33C65 |
Appell, Horn and Lauricella functions
[xref: 43A90]
| 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 and algebras, and related topics
[xref: 05E15, 22E30]
| 33C90 |
Applications
| 33C99 |
None of the above, but in this section
| |
33Dxx
| Basic hypergeometric functions
[xref: 05A15, 39A13]
| 33D05 |
$q$-gamma functions, $q$-beta functions and integrals
| 33D15 |
Basic hypergeometric functions in one variable, ${}_r\phi_s$
| 33D45 |
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
[xref: 05E35, 42C05]
| 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 |
Lamé, Mathieu, and spheroidal wave functions
| 33E12 |
Mittag-Leffler functions and generalizations
| 33E15 |
Other wave functions
| 33E17 |
Painlevé-type functions
| 33E20 |
Other functions defined by series and integrals
| 33E30 |
Other functions coming from differential, difference and integral equations
| 33E50 |
Special functions in characteristic $p$ (gamma functions, etc.)
| 33E99 |
None of the above, but in this section
| |
33Fxx
| Computational aspects
| 33F05 |
Numerical approximation [See also 65D20]
[xref: 65D20]
| 33F10 |
Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also 68W30]
[xref: 68W30]
| 33F99 |
None of the above, but in this section
| |