wolfram {hypergeo} | R Documentation |
Various functions taken from the Wolfram Functions Site
Description
Various functions taken from the Wolfram Functions Site
Usage
w07.23.06.0026.01(A, n, m, z, tol = 0, maxiter = 2000, method = "a")
w07.23.06.0026.01_bit1(A, n, m, z, tol = 0)
w07.23.06.0026.01_bit2(A, n, m, z, tol = 0, maxiter = 2000)
w07.23.06.0026.01_bit3_a(A, n, m, z, tol = 0)
w07.23.06.0026.01_bit3_b(A, n, m, z, tol = 0)
w07.23.06.0026.01_bit3_c(A, n, m, z, tol = 0)
w07.23.06.0029.01(A, n, m, z, tol = 0, maxiter = 2000)
w07.23.06.0031.01(A, n, m, z, tol = 0, maxiter = 2000)
w07.23.06.0031.01_bit1(A, n, m, z, tol = 0, maxiter = 2000)
w07.23.06.0031.01_bit2(A, n, m, z, tol = 0, maxiter = 2000)
Arguments
A |
Parameter of hypergeometric function |
m , n |
Integers |
z |
Primary complex argument |
tol , maxiter |
Numerical arguments as per |
method |
Character, specifying method to be used |
Details
The method
argument is described at f15.3.10
. All
functions' names follow the conventions in
Hypergeometric2F1.pdf
.
Function
w07.23.06.0026.01(A, n, m, z)
returns{}_2F_1(A,A+n,A+m,z)
wherem
andn
are nonnegative integers withm\geq n
.Function
w07.23.06.0029.01(A, n, m, z)
returns{}_2F_1(A,A+n,A-m,z)
.Function
w07.23.06.0031.01(A, n, m, z)
returns{}_2F_1(A,A+n,A+m,z)
withm\leq n
.
Note
These functions use the psigamma()
function which does not yet
take complex arguments; this means that complex values for A
are not supported. I'm working on it.
Author(s)
Robin K. S. Hankin
References
http://functions.wolfram.com/Hypergeometric2F1.pdf
See Also
Examples
# Here we catch some answers from Maple (jjM) and compare it with R's:
jjM <- 0.95437201847068289095 + 0.80868687461954479439i # Maple's answer
jjR <- w07.23.06.0026.01(A=1.1 , n=1 , m=4 , z=1+1i)
# [In practice, one would type 'hypergeo(1.1, 2.1, 5.1, 1+1i)']
stopifnot(Mod(jjM - jjR) < 1e-10)
jjM <- -0.25955090546083991160e-3 - 0.59642767921444716242e-3i
jjR <- w07.23.06.0029.01(A=4.1 , n=1 , m=1 , z=1+4i)
# [In practice, one would type 'hypergeo(4.1, 3.1, 5.1, 1+1i)']
stopifnot(Mod(jjM - jjR) < 1e-15)
jjM <- 0.33186808222278923715e-1 - 0.40188208572232037363e-1i
jjR <- w07.23.06.0031.01(6.7,2,1,2+1i)
# [In practice, one would type 'hypergeo(6.7, 8.7, 7.7, 2+1i)']
stopifnot(Mod(jjM - jjR) < 1e-10)