shanks {hypergeo} | R Documentation |
Evaluation of the hypergeometric function using Shanks's method
Description
Evaluation of the hypergeometric function using Shanks transformation of successive sums
Usage
hypergeo_shanks(A,B,C,z,maxiter=20)
genhypergeo_shanks(U,L,z,maxiter=20)
shanks(Last,This,Next)
Arguments
A , B , C |
Parameters (real or complex) |
U , L |
Upper and lower vectors |
z |
Primary complex argument |
maxiter |
Maximum number of iterations |
Last , This , Next |
Three successive convergents |
Details
The Shanks transformation of successive partial sums is
S(n)=\frac{A_{n+1}A_{n-1}-A_n^2}{A_{n+1}-2A_n+A_{n-1}}
and if the A_n
tend to a limit then the sequence S(n)
often converges more rapidly than A_n
. However, the denominator
is susceptible to catastrophic rounding under fixed-precision
arithmetic and it is difficult to know when to stop iterating.
Note
The
Author(s)
Robin K. S. Hankin
References
Shanks, D. (1955). “Non-linear transformation of divergent and slowly convergent sequences”, Journal of Mathematics and Physics 34:1-42
See Also
Examples
hypergeo_shanks(1/2,1/3,pi,z= 0.1+0.2i)
[Package hypergeo version 1.2-13 Index]