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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 Riemann–Siegel theta function ： ウィキペディア英語版 Riemann–Siegel theta function In mathematics, the Riemann–Siegel theta function is defined in terms of the Gamma function as :$\backslash theta(t)\; =\; \backslash arg\; \backslash left($ \Gamma\left(\frac\right) \right) - \frac t for real values of t. Here the argument is chosen in such a way that a continuous function is obtained and $\backslash theta(0)=0$ holds, i.e., in the same way that the principal branch of the log Gamma function is defined. It has an asymptotic expansion :$\backslash theta(t)\; \backslash sim\; \backslash frac\backslash log\; \backslash frac\; -\; \backslash frac\; -\; \backslash frac+\backslash frac+\; \backslash frac+\backslash cdots$ which is not convergent, but whose first few terms give a good approximation for $t\; \backslash gg\; 1$. Its Taylor-series at 0 which converges for is $\backslash theta(t)\; =\; -\backslash frac\; \backslash log\; \backslash pi\; +\; \backslash sum\_^\; \backslash frac\backslash right)\; \}\; \backslash left(\backslash frac\backslash right)^$ where $\backslash psi^$ denotes the Polygamma function of order $2k$. The Riemann–Siegel theta function is of interest in studying the Riemann zeta function, since it can rotate the Riemann zeta function such that it becomes the totally real valued Z function on the critical line $s\; =\; 1/2\; +\; i\; t$ . == Curve discussion == The Riemann–Siegel theta function is an odd real analytic function for real values of ''t''. It has 3 roots at 0 and $\backslash pm\; 17.8455995405\backslash ldots$ and it is an increasing function for values |''t''| > 6.29, because it has exactly one minima and one maxima at $\backslash pm\; 6.289835988\backslash ldots$ with absolute value $$ 3.530972829\ldots. Lastly it has a unique inflection point at t=0 with $\backslash theta^\backslash prime(0)=\; -\backslash frac\; =\; -2.6860917\backslash ldots$ where the theta function has its derivation minimum. 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「Riemann–Siegel theta 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.