f15.3.1 {hypergeo} | R Documentation |
Hypergeometric function using Euler's integral representation, evaluated using the numerical contour integrals
f15.3.1(A, B, C, z, h = 0)
A,B,C |
Parameters |
z |
Primary complex argument |
h |
specification for the path to be taken; see 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.
The Mellin-Barnes form is not yet coded up.
Robin K. S. Hankin
M. Abramowitz and I. A. Stegun 1965. Handbook of mathematical functions. New York: Dover
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)