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
hypergeometric2F1(a, b, c, z, method = "Cephes", log = TRUE)if log=T returns the log of the 2F1 function; otherwise the 2F1 function.
arbitrary
Must be greater 0
Must be greater than b if |z| < 1, and c > b + a if z = 1
|z| <= 1
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)).
if TRUE, return log(2F1)
Merlise Clyde (clyde@duke.edu)
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.
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. 103:410-423.
tools:::Rd_expr_doi("10.1198/016214507000001337")
Other special functions:
hypergeometric1F1(),
phi1(),
trCCH()
hypergeometric2F1(12, 1, 2, .65)
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