f15.3.1 {hypergeo}R Documentation

Hypergeometric function using Euler's integral representation

Description

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

Usage

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.

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<=q i<=q 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

See Also

hypergeo

Examples


f <- function(h){f15.3.1(1,2,3, z=2, h=h)}

# Winding number [around 1/z] matters:
f(0.5)
f(c(1-1i, 1+1i, -2i))

# Accuracy isn't too bad; compare numerical to analytical result :
f(0.5) - (-1+1i*pi/2)


[Package hypergeo version 1.1-8 Index]