R: Evaluation of the hypergeometric function using Shanks's...

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

`buhring`

### Examples

    hypergeo_shanks(1/2,1/3,pi,z= 0.1+0.2i)

[Package hypergeo version 1.2-13 Index]