Gamma function for complex arguments
Gamma and factorial functions for complex arguments
complex_gamma(z, log = FALSE) complex_factorial(z, log = FALSE) lanczos(z,log=FALSE)
z |
Primary argument, a complex vector |
log |
Boolean, with default |
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
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