hypergeo_cover1 {hypergeo} | R Documentation |
Hypergeometric functions for special values of the parameters
Description
Hypergeometric functions for special values of the parameters
Usage
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)
Arguments
A , B , C |
parameters for the hypergeometric function |
m , n |
Integers (positive or negative) |
z |
Primary complex argument |
tol , maxiter |
Numerical arguments passed to |
method |
Method, passed to |
give |
Boolean with |
Details
These functions deal with the exceptional cases listed on page 559-560.
Function
hypergeo_cover1()
deals with the caseC=A+B\pm m,m=0,1,2,\ldots
Function
hypergeo_cover2()
deals with the caseB=A\pm m,m=0,1,2,\ldots
Function
hypergeo_cover3()
deals with the caseC-A=0,-1,-2,\ldots
[elementary] andC-A=1,2,\ldots
[not covered by AMS-55]
Note
Function hypergeo_cover3()
is required because the
“limiting process” mentioned on p560, just after 15.3.14, is
not explicit. Which is why it dispatches to
w07.23.06.0026.01()
and w07.23.06.0031.01()
,
documented at wolfram
.
Author(s)
Robin K. S. Hankin
References
M. Abramowitz and I. A. Stegun 1965. Handbook of mathematical functions. New York: Dover
See Also
Examples
# 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)