complex_gamma: Gamma function for complex arguments
In hypergeo: The Gauss Hypergeometric Function

Description Usage Arguments Details Author(s) References Examples

Gamma and factorial functions for complex arguments

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

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

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

Robin K. S. Hankin

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.

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