hypergeom (Symbolic Math Toolbox)

Generalized hypergeometric function.

Syntax

hypergeom(n, d, z)

Description

hypergeom(n, d, z) is the generalized hypergeometric function F(n, d, z), also known as the Barnes extended hypergeometric function and denoted by jFk where j = length(n) and k = length(d). For scalar a, b, and c, hypergeom([a,b],c,z) is the Gauss hypergeometric function 2F1(a,b;c;z).

The definition by a formal power series is

where

Either of the first two arguments may be a vector providing the coefficient parameters for a single function evaluation. If the third argument is a vector, the function is evaluated pointwise. The result is numeric if all the arguments are numeric and symbolic if any of the arguments is symbolic.

See Abramowitz and Stegun, Handbook of Mathematical Functions, chapter 15.

Examples

syms a z

hypergeom([],[],z) returns exp(z)

hypergeom(1,[],z) returns -1/(-1+z)

hypergeom(1,2,'z') returns (exp(z)-1)/z

hypergeom([1,2],[2,3],'z') returns -2*(-exp(z)+1+z)/z^2

hypergeom(a,[],z) returns (1-z)^(-a)

hypergeom([],1,-z^2/4) returns besselj(0,z)

hypergeom([-n, n],1/2,(1-z)/2) returns

expand(cos(n*acos(z)))

which is T(n, z), the n-th Chebyshev polynomial.

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