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Biblioteca Dr. Antonio Monteiro · Catálogo |
| 33 | Special functions | ||
| 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 | ||
| 33-04 | Explicit machine computation and programs (not the theory of computation or programming) | ||
| 33-06 | Proceedings, conferences, collections, etc. | ||
| 33-99 | Special functions (33-XX deals with the properties of functions as functions) (not classified at a more specific level) | ||
| 33B | 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 | ||
| 33C | 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 of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions] | ||
| 33C47 | Other special orthogonal polynomials and functions | ||
| 33C50 | Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable | ||
| 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 | ||
| 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 | ||
| 33C90 | Applications | ||
| 33C99 | None of the above, but in this section | ||
| 33D | Basic hypergeometric functions | ||
| 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.) | ||
| 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 | ||
| 33E | 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 | ||
| 33F | 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 | ||
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