wolfram: Various functions taken from the Wolfram Functions Site

In RobinHankin/hypergeo: The Gauss Hypergeometric Function

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 genhypergeo()
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) where m and n are nonnegative integers with m\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) with m\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/PDF/Hypergeometric2F1.pdf

See Also

f15.3.10,hypergeo

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)

RobinHankin/hypergeo documentation built on Aug. 29, 2023, 4 p.m.