著者

中嶋 眞澄

出版者

鹿児島国際大学

雑誌

鹿児島経済論集 (ISSN:13460226)

巻号頁・発行日

vol.47, no.3, pp.147-164, 2006-12

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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.

著者

中嶋 眞澄 ナカジマ マスミ Masumi Nakajima

出版者

鹿児島国際大学経済学部学会

雑誌

鹿児島経済論集 = The Kagoshima journal of economics (ISSN:13460226)

巻号頁・発行日

vol.61, no.3, pp.123-131, 2020-12-27

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We prover here K.Pearson's chi-square test for goodness of fit elementarily.

著者

中嶋 眞澄

出版者

鹿児島国際大学

雑誌

鹿児島経済論集 (ISSN:13460226)

巻号頁・発行日

vol.46, no.4, pp.305-315, 2006-03

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We derive here the functional equation of the Hurwitz zeta-function by direct use of Poisson's summation formula without Mellin transform which is implicitly suggested in the famous book by A. Zygmund [Z] or in the paper of H. Weyl of 1917 [W].

著者

中嶋 眞澄

出版者

鹿児島国際大学

雑誌

鹿児島経済論集 (ISSN:13460226)

巻号頁・発行日

vol.45, no.1, pp.1-5, 2004-06-20

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A simple proof of the strong law of large numbers is given without using Kolmogorov's inequality, Borel-Cantelli's theorem, the existence of the fourth moments of the random variables and so on.