La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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33-XX 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.
• 33-99 Special functions (not classified at a more specific level)
• 33Bxx Elementary classical functions
• 33Cxx Hypergeometric functions
  • 33C05 Classical hypergeometric functions, ₂F₁
  • 33C10 Bessel and Airy functions, cylinder functions, ₀F₁
  • 33C15 Confluent hypergeometric functions, Whittaker functions, ₁F₁
  • 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]
  • 33C47 Other special orthogonal polynomials and functions [Nouveau code MSC 2000]
    • Code MSC1991 affilié : 33C45
  • 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 [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 33C50, 33C80
  • 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 [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 33C70, 33C80
  • 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
• 33Dxx Basic hypergeometric functions
• 33Exx Other special functions
• 33Fxx Computational aspects

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