Unified treatment for the evaluation of generalized complete and incomplete gamma functions
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摘要
The present work applies the binomial expansion theorems to evaluate the generalized complete and incomplete gamma functions arising in the wave scattering and diffraction theory. A simple and efficient algorithm for the calculation of these functions is developed. Some numerical results are presented for significant mapping examples and they are briefly discussed. The formulas obtained are numerically stable for all values of parameters occurring in generalized complete and incomplete gamma functions.
论文关键词：Gamma function,Exponential integral function,Binomial expansion theorem,Scattering and diffraction
论文评审过程：Received 2 December 2005, Revised 13 February 2006, Available online 17 April 2006.
论文官网地址：https://doi.org/10.1016/j.cam.2006.02.038
