gamma_log_complexreturns the value of the logarithm of the gamma function for complex , .
For full information please refer to the NAG Library document for s14ag
The argument of the function.
The value of .
- (errno )
On entry, is ‘too close’ to a non-positive integer when .
gamma_log_complexevaluates an approximation to the logarithm of the gamma function defined for by
where is complex. It is extended to the rest of the complex plane by analytic continuation unless , in which case is real and each of the points is a singularity and a branch point.
gamma_log_complexis based on the method proposed by Kölbig (1972) in which the value of is computed in the different regions of the plane by means of the formulae
where , are Bernoulli numbers (see Abramowitz and Stegun (1972)) and is the largest integer . Note that care is taken to ensure that the imaginary part is computed correctly, and not merely modulo .
The function uses the values and . The remainder term is discussed in Accuracy.
To obtain the value of when is real and positive,
gamma_log_real()can be used.
Abramowitz, M and Stegun, I A, 1972, Handbook of Mathematical Functions, (3rd Edition), Dover Publications
Kölbig, K S, 1972, Programs for computing the logarithm of the gamma function, and the digamma function, for complex arguments, Comp. Phys. Comm. (4), 221–226