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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 Fuchs's theorem ： ウィキペディア英語版 Fuchs' theorem In mathematics, Fuchs' theorem, named after Lazarus Fuchs, states that a second order differential equation of the form :$y\text{'}\text{'}\; +\; p(x)y\text{'}+q(x)y=g(x)\backslash ;$ has a solution expressible by a generalised Frobenius series when $p(x)$, $q(x)$ and $g(x)$ are analytic at $x=a$ or $a$ is a regular singular point. That is, any solution to this second order differential equation can be written as :$y\; =\; \backslash sum\_^\backslash infty\; a\_n\; (x-a)^\; ,\; \backslash quad\; a\_0\; \backslash neq\; 0$ for some real ''s'', or :$y\; =\; y\_0\; \backslash ln\; (x-a)\; +\; \backslash sum\_^\backslash infty\; b\_n(x-a)^,\; \backslash quad\; b\_0\; \backslash neq\; 0$ for some real ''r'', where ''y''0 is a solution of the first kind. Its radius of convergence is at least as large as the minimum of the radii of convergence of $p(x)$, $q(x)$ and $g(x)$. ==See also== *Picard–Fuchs equation 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「Fuchs' theorem」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.