通过 Indigation 的 Gamma 函数 (The Gamma Function via Interpolation)

A new computational framework for evaluation of the gamma function $\Gamma(z)$ over the complex plane is developed. The algorithm is based on interpolation by rational functions, and generalizes the classical methods of Lanczos \cite{Lanczos} and Spouge \cite{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 \cite{AAA,AAA_2020}. The resulting approximations are competitive with Stirling's formula in terms of overall efficiency.

翻译：开发了用于评估复合平面伽马函数$\Gamma(z)美元的新计算框架。算法以理性函数的内推为基础, 并概括了Lanczos\ cite{Lanczos} 和 Spouge \ cite{Spouge} (我们所显示的也是内插的) 的经典方法。这个框架利用了伽马函数的精确极。通过放松这一条件并允许这些极变异, 近于最佳的合理近似是可能的, 这通过在\ cite{AAAA,AAA_ 2020} 中开发的适应性Antoulous Anderson(AAAAAA)算法来证明。由此得出的近似值在总体效率方面与Stirling的公式具有竞争力。