翻訳と辞書 Words near each other ・ Spratleys Japs ・ Spratly (surname) ・ Spratly Island ・ Spratly Islands ・ Spratly Islands dispute ・ Spratt ・ Spratt Cemetery ・ Spratt Model 107 ・ Spratt Stadium ・ Spratt's ・ Spratt's Complex ・ Spratticeps ・ Spratton ・ Spoudaiogeloion ・ Spouge ・ Spouge's approximation ・ Spounalikevirus ・ Spounavirinae ・ Spousal privilege ・ Spouse ・ Spouse for House ・ Spouse of President of Iran ・ Spouse of the Deputy Prime Minister of Malaysia ・ Spouse of the Governor-General of Australia ・ Spouse of the President of India ・ Spouse of the President of the People's Republic of China ・ Spouse of the Prime Minister of Australia ・ Spouse of the Prime Minister of Cambodia ・ Spouse of the Prime Minister of Canada ・ Spouse of the Prime Minister of India Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Spouge's approximation ： ウィキペディア英語版 Spouge's approximation In mathematics, Spouge's approximation is a formula for the gamma function due to John L. Spouge in 1994. The formula is a modification of Stirling's approximation, and has the form :$\backslash Gamma(z+1)\; =\; (z+a)^\; e^\; \backslash left(c\_0\; +\; \backslash sum\_^\; \backslash frac\; +\; \backslash varepsilon\_a(z)\; \backslash right)$ where ''a'' is an arbitrary positive integer and the coefficients are given by :$c\_0\; =\; \backslash sqrt\backslash ,$ :$c\_k\; =\; \backslash frac\; (-k+a)^\; e^\; \backslash quad\; k\backslash in\backslash .$ Spouge has proved that, if Re(''z'') > 0 and ''a'' > 2, the relative error in discarding ε''a''(''z'') is bounded by :$\backslash ,a^\; (2\; \backslash pi)^.$ The formula is similar to the Lanczos approximation, but has some distinct features. Whereas the Lanczos formula exhibits faster convergence, Spouge's coefficients are much easier to calculate and the error can be set arbitrarily low. The formula is therefore feasible for arbitrary-precision evaluation of the gamma function. However, special care must be taken to use sufficient precision when computing the sum due to the large size of the coefficients $c\_k$, as well as their alternating sign. For example, for ''a''=49, you must compute the sum using about 65 decimal digits of precision in order to obtain the promised 40 decimal digits of accuracy. ==See also== * Stirling's approximation * Lanczos approximation 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Spouge's approximation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.