The Gamma Function via Interpolation
Abstract
A new computational framework for evaluation of the gamma function (z) over the complex plane is developed. The algorithm is based on interpolation by rational functions, and generalizes the classical methods of Lanczos Lanczos and Spouge Spouge (which we show are also interpolatory). This framework utilizes the exact poles of the gamma function. By relaxing this condition and allowing the poles to vary, a near-optimal rational approximation is possible, which is demonstrated using the adaptive Antoulous Anderson (AAA) algorithm, developed in AAA,AAA2020. The resulting approximations are competitive with Stirling's formula in terms of overall efficiency.
0