hypergeo_contfrac: Continued fraction expansion of the hypergeometric function

In RobinHankin/hypergeo: The Gauss Hypergeometric Function

Continued fraction expansion of the hypergeometric function

Description

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

Usage

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

Arguments

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

Details

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.

Note

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.

Author(s)

Robin K. S. Hankin

References

• M. Abramowitz and I. A. Stegun 1965. Handbook of mathematical functions. New York: Dover

• http://functions.wolfram.com/PDF/Hypergeometric2F1.pdf

See Also

genhypergeo

Examples

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

RobinHankin/hypergeo documentation built on July 18, 2024, 9:49 p.m.