# f15.3.1: Hypergeometric function using Euler's integral representation In hypergeo: The Gauss Hypergeometric Function

## Description

Hypergeometric function using Euler's integral representation, evaluated using numerical contour integrals.

## Usage

 1 f15.3.1(A, B, C, z, h = 0)

## Arguments

 A,B,C Parameters z Primary complex argument h specification for the path to be taken; see details

## Details

Argument h specifies the path to be taken (the path has to avoid the point 1/z). If h is real and of length 1, the path taken comprises two straight lines: one from 0 to 0.5+hi and one from 0.5+hi to 1 (if h=0 the integration is performed over a single segment).

Otherwise, the integration is performed over length(h)+1 segments: 0 to h[1], then h[i] to h[i+1] for 1 <= i <= n-1 and finally h[n] to 1.

See examples and notes sections below.

## Note

The Mellin-Barnes form is not yet coded up.

## Author(s)

Robin K. S. Hankin

## References

M. Abramowitz and I. A. Stegun 1965. Handbook of mathematical functions. New York: Dover