Gamma函数の漸近公式の厳密な別証明 [in Japanese] An alternative rigorous proof of the asymptotic formula of Euler's gamma-function [in Japanese]
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The following asymptotic formula of Euler's Gamma function; [numerical formula] is well-known: [numerical formula] But there seems to be no rigorous proof of it using the saddle point method as far as the author knows, although there are some rigorous proofs using Euler-Maclaurin's summation formula or Poisson's summation formula and so on. In this short paper we will give a rigorous proof of it using the saddle point method as well as a rigorous proof of [numerical formula] by using the same method.
- The Kagoshima journal of economics
The Kagoshima journal of economics 47(3), 147-164, 2006-12
The International University of Kagoshima