翻訳と辞書 Words near each other ・ Argyle Heir ・ Argument from marginal cases ・ Argument from miracles ・ Argument from morality ・ Argument from nonbelief ・ Argument from poor design ・ Argument from queerness ・ Argument from reason ・ Argument from religious experience ・ Argument from silence ・ Argument in the alternative ・ Argument map ・ Argument of a function ・ Argument of latitude ・ Argument of periapsis ・ Argument principle ・ Argument shift method ・ Argument to moderation ・ Argument-deduction-proof distinctions ・ Argument-dependent name lookup ・ Argumental ・ Argumentation and Advocacy ・ Argumentation and Debate ・ Argumentation ethics ・ Argumentation framework ・ Argumentation theory ・ Argumentative ・ Argumentative dialogue ・ Argumentative turn ・ Arguments for and against drug prohibition 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 Argument principle ： ウィキペディア英語版 Argument principle In complex analysis, the argument principle (or Cauchy's argument principle) relates the difference between the number of zeros and poles of a meromorphic function to a contour integral of the function's logarithmic derivative. Specifically, if ''f''(''z'') is a meromorphic function inside and on some closed contour ''C'', and ''f'' has no zeros or poles on ''C'', then : $\backslash oint\_\; \backslash ,\; dz=2\backslash pi\; i\; (N-P)$ where ''N'' and ''P'' denote respectively the number of zeros and poles of ''f''(''z'') inside the contour ''C'', with each zero and pole counted as many times as its multiplicity and order, respectively, indicate. This statement of the theorem assumes that the contour ''C'' is simple, that is, without self-intersections, and that it is oriented counter-clockwise. More generally, suppose that ''f''(''z'') is a meromorphic function on an open set Ω in the complex plane and that ''C'' is a closed curve in Ω which avoids all zeros and poles of ''f'' and is contractible to a point inside Ω. For each point ''z'' ∈ Ω, let ''n''(''C'',''z'') be the winding number of ''C'' around ''z''. Then :$\backslash oint\_\; \backslash frac\backslash ,\; dz\; =\; 2\backslash pi\; i\; \backslash left(\backslash sum\_a\; n(C,a)\; -\; \backslash sum\_b\; n(C,b)\backslash right)$ where the first summation is over all zeros ''a'' of ''f'' counted with their multiplicities, and the second summation is over the poles ''b'' of ''f'' counted with their orders. ==Interpretation of the contour integral== The contour integral $\backslash oint\_\; \backslash frac\backslash ,\; dz$ can be interpreted in two ways: * as the total change in the argument of ''f''(''z'') as ''z'' travels around ''C'', explaining the name of the theorem; this follows from :$\backslash frac\backslash log(f(z))=\backslash frac$ and the relation between arguments and logarithms. * as 2π''i'' times the winding number of the path ''f''(''C'') around the origin, using the substitution ''w'' = ''f''(''z''): :$\backslash oint\_\; \backslash frac\backslash ,\; dz\; =\; \backslash oint\_\; \backslash frac\backslash ,\; dw$ 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「Argument principle」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.