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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 Nörlund–Rice integral ： ウィキペディア英語版 Nörlund–Rice integral In mathematics, the Nörlund–Rice integral, sometimes called Rice's method, relates the ''n''th forward difference of a function to a line integral on the complex plane. As such, it commonly appears in the theory of finite differences, and also has been applied in computer science and graph theory to estimate binary tree lengths. It is named in honour of Niels Erik Nørlund and Stephen O. Rice. Nørlund's contribution was to define the integral; Rice's contribution was to demonstrate its utility by applying saddle-point techniques to its evaluation. ==Definition== The ''n''th forward difference of a function ''f''(''x'') is given by :$\backslash Delta^n()(x)=\; \backslash sum\_^n\; (-1)^\; f(x+k)$ where $$ is the binomial coefficient. The Nörlund–Rice integral is given by :$\backslash sum\_^n\; (-1)^\; f(k)\; =$ \frac \oint_\gamma \frac\, \mathrmz where ''f'' is understood to be meromorphic, α is an integer, $0\backslash leq\; \backslash alpha\; \backslash leq\; n$, and the contour of integration is understood to circle the poles located at the integers α, ..., ''n'', but none of the poles of ''f''. The integral may also be written as :$\backslash sum\_^n\; (-1)^\; f(k)\; =$ -\frac \oint_\gamma B(n+1, -z) f(z)\, \mathrmz where ''B''(''a'',''b'') is the Euler beta function. If the function $f(z)$ is polynomially bounded on the right hand side of the complex plane, then the contour may be extended to infinity on the right hand side, allowing the transform to be written as :$\backslash sum\_^n\; (-1)^\; f(k)\; =$ \frac \int_^ \frac\, \mathrmz where the constant ''c'' is to the left of α. 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「Nörlund–Rice integral」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.