R: Complex Gamma Function

gammaz {pracma} | R Documentation

## Complex Gamma Function

### Description

Gamma function valid in the entire complex plane.

### Usage

    gammaz(z)

### Arguments

`z` | Real or complex number or a numeric or complex vector.

### Details

Computes the Gamma function for complex arguments using the Lanczos series approximation.

Accuracy is 15 significant digits along the real axis and 13 significant digits elsewhere.

To compute the logarithmic Gamma function use `log(gammaz(z))`.

### Value

Returns a complex vector of function values.

### Note

Copyright (c) 2001 Paul Godfrey for a Matlab version available on Mathwork's Matlab Central under BSD license.

Numerical Recipes used a 7 terms formula for a less effective approximation.

### References

Zhang, Sh., and J. Jin (1996). Computation of Special Functions. Wiley-Interscience, New York.

### See Also

`gamma`, `gsl::lngamma_complex`

### Examples

    max(gamma(1:10) - gammaz(1:10))
    gammaz(-1)
    gammaz(c(-2-2i, -1-1i, 0, 1+1i, 2+2i))

    # Euler's reflection formula
    z <- 1+1i
    gammaz(1-z) * gammaz(z)  # == pi/sin(pi*z)

[Package pracma version 2.0.4 Index]