`hypergeom`

Generalized hypergeometric function.

Category: Mathematics > Mathematical Functions

Syntax

F = hypergeom(a, b, z)

Evaluates pFq with numerator parameters a and denominator parameters b.

Description

The function is the series whose term ratio is a rational function of the index: sum( prod(pochhammer(a,k)) / prod(pochhammer(b,k)) * z^k / k! ). Many special functions are particular cases: hypergeom([], [], z) is exp(z), and with a = [a1 a2], b = c the Gauss function 2F1 results. Convergence of the series for p = q + 1 requires abs(z) < 1, but the function is continued analytically.

Input arguments

a: Vector of p upper parameters; may be empty.
b: Vector of q lower parameters; may be empty.
z: Argument, numeric or symbolic.

Output arguments

F: Array of the same size as z.

Example

Gauss function and exp

hypergeom([1 2], 3, 0.5)
hypergeom([], [], 1)
exp(1)

Output

ans = 1.5452
ans = 2.7183
ans = 2.7183

hypergeom