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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク trigamma function ： ウィキペディア英語版 trigamma function In mathematics, the trigamma function, denoted $\backslash psi\_1(z)$, is the second of the polygamma functions, and is defined by : $\backslash psi\_1(z)\; =\; \backslash frac\; \backslash ln\backslash Gamma(z)$. It follows from this definition that : $\backslash psi\_1(z)\; =\; \backslash frac\; \backslash psi(z)$ where $\backslash psi(z)$ is the digamma function. It may also be defined as the sum of the series : $\backslash psi\_1(z)\; =\; \backslash sum\_^\backslash frac,$ making it a special case of the Hurwitz zeta function : $\backslash psi\_1(z)\; =\; \backslash zeta(2,z).\; \backslash frac\{\}\{\}$ Note that the last two formulæ are valid when $1-z$ is not a natural number. ==Calculation== A double integral representation, as an alternative to the ones given above, may be derived from the series representation: : $\backslash psi\_1(z)\; =\; \backslash int\_0^1\backslash int\_0^y\backslash frac\backslash ,dx\backslash ,dy$ using the formula for the sum of a geometric series. Integration by parts yields: : $\backslash psi\_1(z)\; =\; -\backslash int\_0^1\backslash frac\}\backslash ,dx$ An asymptotic expansion as a ウィキペディア（Wikipedia）』 ■ウィキペディアで「trigamma 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.