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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 Power series solution of differential equations ： ウィキペディア英語版 Power series solution of differential equations In mathematics, the power series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients. == Method == Consider the second-order linear differential equation : $a\_2(z)f\text{'}\text{'}(z)+a\_1(z)f\text{'}(z)+a\_0(z)f(z)=0.\backslash ;\backslash !$ Suppose ''a''2 is nonzero for all ''z''. Then we can divide throughout to obtain : $f\text{'}\text{'}+f\text{'}+f=0.$ Suppose further that ''a''1/''a''2 and ''a''0/''a''2 are analytic functions. The power series method calls for the construction of a power series solution :$f=\backslash sum\_^\backslash infty\; A\_kz^k.$ If ''a''2 is zero for some ''z'', then the Frobenius method, a variation on this method, is suited to deal with so called ''singular points''. The method works analogously for higher order equations as well as for systems. 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「Power series solution of differential equations」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.