33XX 


Special functions (33XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for numbertheoretic aspects see 11XX; for representation theory see 22Exx} 

33Cxx 

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 ($E$, $G$, $H$ and $I$ 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 