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 2.4.4 Index]