Complex Gamma Function
Gamma function valid in the entire complex plane.
gammaz(z)
z |
Real or complex number or a numeric or complex vector. |
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)).
Returns a complex vector of function values.
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.
Zhang, Sh., and J. Jin (1996). Computation of Special Functions. Wiley-Interscience, New York.
gamma, gsl::lngamma_complex
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)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.