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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 reflection formula ： ウィキペディア英語版 reflection formula In mathematics, a reflection formula or reflection relation for a function ''f'' is a relationship between ''f''(''a'' − ''x'') and ''f''(''x''). It is a special case of a functional equation, and it is very common in the literature to use the term "functional equation" when "reflection formula" is meant. Reflection formulas are useful for numerical computation of special functions. In effect, an approximation that has greater accuracy or only converges on one side of a reflection point (typically in the positive half of the complex plane) can be employed for all arguments. == Known formula == The even and odd functions satisfy simple reflection relations around ''a'' = 0. For all even functions, :$f(-x)\; =\; f(x),\backslash ,\backslash !$ and for all odd functions, :$f(-x)\; =\; -f(x).\backslash ,\backslash !$ A famous relationship is Euler's reflection formula :$\backslash Gamma(z)\backslash Gamma(1-z)\; =\; \backslash frac\; (1-z)+(-1)^\backslash psi^\; (z)\; =\; (-1)^n\; \backslash pi\; \backslash frac\; \backslash cot\; \backslash ,$ which springs trivially from the fact that the polygamma functions are defined as the derivations of the $\backslash ln\; \backslash Gamma$ and thus its reflection formula is inherited to them. The Riemann zeta function ζ(''z'') satisfies :$\backslash frac\; =\; \backslash frac\backslash right),\backslash ,\backslash !$ and the Riemann Xi function ξ(''z'') satisfies :$\backslash xi(z)\; =\; \backslash xi(1-z).\; \backslash ,\backslash !$ 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「reflection formula」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.