R: Transformations of the hypergeometric function

f15.3.10 {hypergeo} | R Documentation

## Transformations of the hypergeometric function

### Description

Transformations of the hypergeometric function detailed in AMS-55, page 559-560.

### Usage

    f15.3.10       (A, B,    z, tol = 0, maxiter = 2000, method = "a")
    f15.3.10_a     (A, B,    z, tol = 0, maxiter = 2000              )
    f15.3.10_b     (A, B,    z, tol = 0, maxiter = 2000              )
    f15.3.11       (A, B, m, z, tol = 0, maxiter = 2000, method = "a")
    f15.3.11_bit1  (A, B, m, z, tol = 0                              )
    f15.3.11_bit2_a(A, B, m, z, tol = 0, maxiter = 2000              )
    f15.3.11_bit2_b(A, B, m, z, tol = 0, maxiter = 2000              )
    f15.3.12       (A, B, m, z, tol = 0, maxiter = 2000, method = "a")
    f15.3.12_bit1  (A, B, m, z, tol = 0                              )
    f15.3.12_bit2_a(A, B, m, z, tol = 0, maxiter = 2000              )
    f15.3.12_bit2_b(A, B, m, z, tol = 0, maxiter = 2000              )
    f15.3.13       (A, C,    z, tol = 0, maxiter = 2000, method = "a")
    f15.3.13_a     (A, C,    z, tol = 0, maxiter = 2000              )
    f15.3.13_b     (A, C,    z, tol = 0, maxiter = 2000              )
    f15.3.14       (A, C, m, z, tol = 0, maxiter = 2000, method = "a")
    f15.3.14_bit1_a(A, C, m, z, tol = 0, maxiter = 2000              )
    f15.3.14_bit1_b(A, C, m, z, tol = 0, maxiter = 2000              )
    f15.3.14_bit2  (A, C, m, z, tol = 0                              )
    f15.3.13_14    (A, C, m, z, tol = 0, maxiter = 2000, method = "a")
    f15.3.10_11_12 (A, B, m, z, tol = 0, maxiter = 2000, method = "a")
    f15.1.1        (A, B, C, z, tol = 0, maxiter = 2000              )

### Arguments

`A,B,C` | Parameters of the hypergeometric function
`m` | Integer linking `A`, `B`, `C` as set out in AMS-55, page 559,560
`z` | primary complex argument
`tol,maxiter` | numerical parameters
`method` | Length 1 character vector specifying the method. See details

### Details

Naming scheme (functions and arguments) follows AMS-55, pages 559-560.

The `method` argument to (eg) `f15.3.14()` specifies whether to use `psigamma()` directly (method “`a`”), or the recurrence 6.3.5 (method “`b`”). Press et al recommend method “`b`”, presumably on the grounds of execution speed. I'm not so sure (method “`a`” seems to be more accurate in the sense that it returns values closer to those of Maple).

Method “`c`” means to use a totally dull, slow, direct (but clearly correct) summation, for the purposes of debugging. This is only used for the functions documented under `wolfram.Rd`

Functions `f15.3.13_14()` and `f15.3.10_11_12()` are convenience wrappers. For example, function `f15.3.13_14()` dispatches to either `f15.3.13()` or `f15.3.14()` depending on the value of `m`.

### Note

These functions are not really designed to be called by the user: use `hypergeo()` instead, or `hypergeo_cover[123]()` for specific cases.

### Author(s)

Robin K. S. Hankin

### References

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

### See Also

`hypergeo`,`wolfram`,`hypergeo_cover1`

### Examples

    f15.3.10_11_12(A=1.1, B=pi, m= +3, z=.1+.1i)
    f15.3.10_11_12(A=1.1, B=pi, m= -3, z=.1+.1i)

[Package hypergeo version 1.2-13 Index]