hypergeo_cover1 {hypergeo} | R Documentation |
Hypergeometric functions for special values of the parameters
hypergeo_cover1(A, B, m, z, tol = 0, maxiter = 2000, method = "a", give = FALSE) hypergeo_cover2(A, C, m, z, tol = 0, maxiter = 2000, method = "a", give = FALSE) hypergeo_cover3(A, n, m, z, tol = 0, maxiter = 2000, method = "a", give = FALSE)
A,B,C |
parameters for the hypergeometric function |
m,n |
Integers (positive or negative) |
z |
Primary complex argument |
tol,maxiter |
Numerical arguments passed to genhypergeo() |
method |
Method, passed to f15.3.10() (qv) |
give |
Boolean with TRUE meaning to return the choice of
function used and default FALSE meaning to return the
function's evaluate |
These functions deal with the exceptional cases listed on page 559-560.
hypergeo_cover1()
deals with the case
C=A+B +/- m, m=0,1,2,...
hypergeo_cover2()
deals with the case
B=A +/- m, m=0,1,2,...
hypergeo_cover3()
deals with the case
C-A=0,-1,-2,... [elementary] and
C-A=1,2,... [not covered by AMS-55]
Robin K. S. Hankin
M. Abramowitz and I. A. Stegun 1965. Handbook of mathematical functions. New York: Dover
# Test hypergeo_cover1(): jjR <- hypergeo(pi,pi/2,3*pi/2-4, z=0.1+0.2i) jjM <- 0.53745229690249593045 + 1.8917456473240515664i # Test hypergeo_cover2(): jjM <- -0.15888831928748121465e-5 + 0.40339599711492215912e-4i jjR <- hypergeo(pi,pi+2, 1.1 , 1+10i) # This is 15.3.13 stopifnot(Mod(jjR-jjM)<1e-10) # Test hypergeo_cover3() jjM <- -0.24397135980533720308e-1 + 0.28819643319432922231i jjR <- hypergeo(pi, 1.4, pi+4, 1+6i) stopifnot(Mod(jjR-jjM)<1e-10)