关于倒数 Gamma 函数的幂级数展开
数论
2017-01-16 v4
摘要
利用 Gamma 函数的反射公式，我们推导出了倒数 Gamma 函数泰勒系数的一个新公式。该新公式即使对于非常小的索引值也能提供有效的系数渐近值。文中给出了符号振荡以及主导增长阶。
引用
@article{arxiv.1407.5983,
title = {On the Power Series Expansion of the Reciprocal Gamma Function},
author = {Lazhar Fekih-Ahmed},
journal= {arXiv preprint arXiv:1407.5983},
year = {2017}
}
备注
Corrected a sign in equation (3.21) due to a minor error in (3.19) where the fraction was inadvertently inverted. Now the rough approximation provides an elementary proof that the order of the reciprocal gamma function is 1 and that its type is maximal