翻訳と辞書 Words near each other ・ Resistance Memorial Cross ・ Resistance movement ・ Resistance movement in Auschwitz ・ Residual value ・ Residual-current device ・ Residual-excited linear prediction ・ Residual-resistance ratio ・ Residually finite group ・ ResidualVM ・ Residuary estate ・ Residuated Boolean algebra ・ Residuated lattice ・ Residuated mapping ・ Residue ・ Residue (chemistry) ・ Residue (complex analysis) ・ Residue at infinity ・ Residue curve ・ Residue depth ・ Residue field ・ Residue Hymns ・ Residue numeral system ・ Residue of The Residents ・ Residue theorem ・ Residue-class-wise affine group ・ Residuum (geology) ・ Resighini Rancheria ・ Resign-to-run laws ・ Resignation ・ Resignation (disambiguation) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Residue (complex analysis) ： ウィキペディア英語版 Residue (complex analysis) In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function $f:\; \backslash mathbb\; \backslash setminus\; \backslash \_k\; \backslash rightarrow\; \backslash mathbb$ that is holomorphic except at the discrete points ''k'', even if some of them are essential singularities.) Residues can be computed quite easily and, once known, allow the determination of general contour integrals via the residue theorem. == Definition == The residue of a meromorphic function $f$ at an isolated singularity $a$, often denoted $\backslash operatorname(f,a)$ or $\backslash operatorname\_a(f)$, is the unique value $R$ such that $f(z)-\; R/(z-a)$ has an analytic antiderivative in a punctured disk . Alternatively, residues can be calculated by finding Laurent series expansions, and one can define the residue as the coefficient a-1 of a Laurent series. The definition of a residue can be generalized to arbitrary Riemann surfaces. Suppose $\backslash omega$ is a 1-form on a Riemann surface. Let $\backslash omega$ be meromorphic at some point $x$, so that we may write $\backslash omega$ in local coordinates as $f(z)\; \backslash ;\; dz$. Then the residue of $\backslash omega$ at $x$ is defined to be the residue of $f(z)$ at the point corresponding to $x$. 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「Residue (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.