A Comparison of Computational Methods and Algorithms for the Complex Gamma Function

This paper presents a survey and comparison of some computational methods and algorithms for gamma and log-gamma functions of complex arguments. All these methods and algorithms have been reported recently in the open literature and include Chebyshev approximations, Padd expansion, and Stirling's asymptotic series. The comparison leads to the conclusion that ACM Algorithm 421 by H. Kuki is the best program either for individual application or for inclusion in subroutine libraries.