翻訳と辞書 Words near each other ・ Q-construction ・ Q-D-Š ・ Q-dance ・ Q-derivative ・ Q-difference polynomial ・ Q-expansion principle ・ Q-exponential ・ Q-exponential distribution ・ Q-Factor (LGBT) ・ Q-Feel ・ Q-FISH ・ Q-Flex ・ Q-Free ・ Q-function ・ Q-Games ・ Q-gamma function ・ Q-Gaussian distribution ・ Q-Genz ・ Q-go ・ Q-guidance ・ Q-Hahn polynomials ・ Q-in-Law ・ Q-Jacobi polynomials ・ Q-Konhauser polynomials ・ Q-Krawtchouk polynomials ・ Q-Laguerre polynomials ・ Q-LAN ・ Q-learning ・ Q-Less ・ Q-Lets and Co. 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 Q-gamma function ： ウィキペディア英語版 Q-gamma function In q-analog theory, the q-gamma function, or basic gamma function, is a generalization of the ordinary Gamma function closely related to the double gamma function. It was introduced by . It is given by :$\backslash Gamma\_q(x)\; =\; (1-q)^\backslash prod\_^\backslash infty$ \frac}=(1-q)^\,\frac when |q|<1, and : $\backslash Gamma\_q(x)=\backslash frac)\_\backslash infty\})\_\backslash infty\}(q-1)^q^\}$ if |q|>1. Here (·;·)∞ is the infinite q-Pochhammer symbol. It satisfies the functional equation :$\backslash Gamma\_q(x+1)\; =\; \backslash frac\backslash Gamma\_q(x)=()\_q\backslash Gamma\_q(x)$ For non-negative integers ''n'', :$\backslash Gamma\_q(n)=()\_q!$ where ()''q''! is the q-factorial function. Alternatively, this can be taken as an extension of the q-factorial function to the real number system. The relation to the ordinary gamma function is made explicit in the limit :$\backslash lim\_\; \backslash Gamma\_q(x)\; =\; \backslash Gamma(x).$ A q-analogue of Stirling's formula for |q|<1 is given by : A q-analogue of the multiplication formula for |q|<1 is given by :$\backslash Gamma\_\backslash left(\backslash frac\; n\backslash right)\backslash Gamma\_\backslash left(\backslash frac\; n\backslash right)\backslash cdots\backslash Gamma\_\backslash left(\backslash frac\; n\backslash right)\; =()\_q^\backslash left(()\_q\; \backslash Gamma^2\_\backslash left(\backslash frac12\backslash right)\backslash right)^\}\backslash Gamma\_q(x).$ Due to I. Mező, the q-analogue of the Raabe formula exists, at least if we use the q-gamma function when |q|>1. With this restriction : $\backslash int\_0^1\backslash log\backslash Gamma\_q(x)dx=\backslash frac+\backslash log\backslash sqrt\}\}+\backslash log(q^;q^)\_\backslash infty\; \backslash quad(q>1).$ ==References== * * *() * 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「Q-gamma function」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.