pracma (version 1.8.8)

gammaz: 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.

Value

• Returns a complex vector of function values.

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)).

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)