hypergeo_contfrac {hypergeo} | R Documentation |
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 |
z |
Complex argument |
tol |
tolerance (passed to |
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
See Also
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