hypergeo_contfrac: Continued fraction expansion of the hypergeometric function
In hypergeo: The Gauss Hypergeometric Function

Description Usage Arguments Details Note Author(s) References See Also Examples

Continued fraction expansion of the hypergeometric and generalized hypergeometric functions using continued fraction expansion.

1 2	hypergeo_contfrac(A, B, C, z, tol = 0, maxiter = 2000) genhypergeo_contfrac_single(U, L, z, tol = 0, maxiter = 2000)

`A,B,C`	Parameters (real or complex)
`U,L`	In function `genhypergeo_contfrac()`, upper and lower arguments as in `genhypergeo()`
`z`	Complex argument
`tol`	tolerance (passed to `GCF()`)
`maxiter`	maximum number of iterations

These functions are included in the package in the interests of completeness, but it is not clear when it is advantageous to use continued fraction form rather than the series form.

The continued fraction expression is the RHS identity 07.23.10.0001.01 of Hypergeometric2F1.pdf.

The function sometimes fails to converge to the correct value but no warning is given.

Function genhypergeo_contfrac() is documented under genhypergeo.Rd.

Robin K. S. Hankin

M. Abramowitz and I. A. Stegun 1965. Handbook of mathematical functions. New York: Dover
http://functions.wolfram.com/Hypergeometric2F1.pdf

genhypergeo

hypergeo_contfrac(0.3 , 0.6 , 3.3 , 0.1+0.3i)
# Compare Maple: 1.0042808294775511972+0.17044041575976110947e-1i

genhypergeo_contfrac_single(U=0.2 , L=c(9.9,2.7,8.7) , z=1+10i)
# (powerseries does not converge)
# Compare Maple: 1.0007289707983569879 + 0.86250714217251837317e-2i