R: Continued fraction expansion of the hypergeometric function

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 `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/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

[Package hypergeo version 1.2-13 Index]