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BAS (version 0.90)

hypergeometric2F1: Gaussian hypergeometric2F1 function

Description

Compute the Gaussian Hypergeometric2F1 function: 2F1(a,b,c,z) = Gamma(b-c) Int_0^1 t^(b-1) (1 - t)^(c -b -1) (1 - t z)^(-a) dt

Usage

hypergeometric2F1(a,b,c,z, method="Cephes", log=TRUE)

Arguments

a
arbitrary
b
Must be greater 0
c
Must be greater than b if |z| < 1, and c > b + a if z = 1
z
|z|
method
The default is to use the Cephes library routine. This sometimes is unstable for large a or z near one returning Inf or negative values. In this case, try method="Laplace", which use a Laplace approximation for tau = exp(t/(1-t)).
log
if TRUE, return log(2F1)

Value

  • if log=T returns the log of the 2F1 function; otherwise the 2F1 function.

Details

The default is to use the routine hyp2f1.c from the Cephes library. If that return a negative value or Inf, one should try method="Laplace" which is based on the Laplace approximation as described in Liang et al JASA 2008. This is used in the hyper-g prior to calculate marginal likelihoods.

References

Cephes library hyp2f1.c Liang, F., Paulo, R., Molina, G., Clyde, M. and Berger, J.O. (2005) Mixtures of g-priors for Bayesian Variable Selection. Journal of the American Statistical Association http://www.stat.duke.edu/05-12.pdf

Examples

Run this code
hypergeometric2F1(12,1,2,.65)

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