R: Gamma function for complex arguments

complex_gamma {hypergeo} | R Documentation

## Gamma function for complex arguments

### Description

Gamma and factorial functions for complex arguments

### Usage

    complex_gamma(z, log = FALSE)
    complex_factorial(z, log = FALSE)
    lanczos(z,log=FALSE)

### Arguments

`z` | Primary argument, a complex vector
`log` | Boolean, with default `FALSE` meaning to return the function value and `TRUE` meaning to return its logarithm

### Details

Method follows that of Lanczos, coefficients identical to those of the GSL

### Author(s)

Robin K. S. Hankin

### References

Lanczos, C. 1964. “A precision approximation of the gamma function”. Journal of the society for industrial and applied mathematics series B, Volume 1, pp86-96

M. Galassi et al, GNU Scientific Library Reference Manual (3rd Ed.), ISBN 0954612078.

### Examples

    complex_gamma(5)  # should be 4!=24

    complex_gamma(1+1i)   # takes complex arguments

    complex_gamma(-5/2) + sqrt(pi)*8/15  # should be small

    z <- pi + 1i*sqrt(2)
    complex_gamma(z+1)-z*complex_gamma(z)   # should be small

    complex_gamma(z)*complex_gamma(1-z) - pi/sin(pi*z)  # small

[Package hypergeo version 1.2-13 Index]