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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 Partial fractions in complex analysis ： ウィキペディア英語版 Partial fractions in complex analysis In complex analysis, a partial fraction expansion is a way of writing a meromorphic function ''f(z)'' as an infinite sum of rational functions and polynomials. When ''f(z)'' is a rational function, this reduces to the usual method of partial fractions. ==Motivation== By using polynomial long division and the partial fraction technique from algebra, any rational function can be written as a sum of terms of the form ''1 / (az + b)k'' + ''p(z)'', where ''a'' and ''b'' are complex, ''k'' is an integer, and ''p(z)'' is a polynomial . Just as polynomial factorization can be generalized to the Weierstrass factorization theorem, there is an analogy to partial fraction expansions for certain meromorphic functions. A proper rational function, i.e. one for which the degree of the denominator is greater than the degree of the numerator, has a partial fraction expansion with no polynomial terms. Similarly, a meromorphic function ''f(z)'' for which |''f(z)''| goes to 0 as ''z'' goes to infinity at least as quickly as |''1/z''|, has an expansion with no polynomial terms. 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「Partial fractions in complex analysis」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.