hyp2f1: Compute the Gaussian hypergeometric function with complex...

In appell: Compute Appell's F1 hypergeometric function

Description

Two different algorithms can be used.

Usage

  hyp2f1(a, b, c, z,
    algorithm = c("michel.stoitsov", "forrey"))

Arguments

a	complex parameter
b	complex parameter
c	complex parameter
z	complex variable
algorithm	either “michel.stoitsov” (default) or “forrey” (see the details)

Details

The first, default, algorithm uses Fortran code in “hyp_2F1.f90” from N. L. J. Michel and M. V. Stoitsov, which is available at http://cpc.cs.qub.ac.uk/summaries/AEAE. The corresponding background reference is N. L. J. Michel and M. V. Stoitsov (2008): Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions, Computer Physics Communications 178:535-551.

The second algorithm uses Fortran code in “cyp.f” from R. C. Forrey is used which is available at http://physics.bk.psu.edu/codes/chyp.f. The corresponding background reference is R. C. Forrey (1997): Computing the hypergeometric function, Journal of Computational Physics 137:79-100.

Value

The complex value of the Gaussian hypergeometric function.

Author(s)

Daniel Sabanes Bove [e-mail]

Examples

## library(appell)

## compare the results of both algorithms
## for random test data.

## todo: add better tests trying to replicate published results? 

nTest <- 100L
set.seed(38)

a <- complex(real=rnorm(nTest),
             imaginary=rnorm(nTest))
b <- complex(real=rnorm(nTest),
             imaginary=rnorm(nTest))
c <- complex(real=rnorm(nTest),
             imaginary=rnorm(nTest))
z <- complex(real=rnorm(nTest),
             imaginary=rnorm(nTest))

tableHyp2f1 <- matrix(nrow=nTest,
                      ncol=2L,
                      dimnames=
                      list(NULL,
                           c("forrey", "michel.stoitsov")))

for(i in seq_len(nTest))
{
    tableHyp2f1[i, "forrey"] <- hyp2f1(a[i], b[i], c[i], z[i],
                                       algorithm="forrey")
    tableHyp2f1[i, "michel.stoitsov"] <- hyp2f1(a[i], b[i], c[i], z[i],
                                                algorithm="michel.stoitsov")
}

tableHyp2f1

abs(tableHyp2f1[, "forrey"] - tableHyp2f1[, "michel.stoitsov"])
## so very small differences,
## at least in this range of function parameters.

appell documentation built on May 2, 2019, 5:51 a.m.