翻訳と辞書 Words near each other ・ Indefatigable (1799 ship) ・ Indefatigable-class battlecruiser ・ Indefeasible rights of use ・ Indefinite ・ Indefinite and fictitious numbers ・ Indefinite detention ・ Indefinite detention without trial ・ Indefinite imprisonment ・ Indefinite inner product space ・ Indefinite leave to remain ・ Indefinite lifespan ・ Indefinite monism ・ Indefinite orthogonal group ・ Indefinite product ・ Indefinite pronoun ・ Indefinite sum ・ Indeg.iul.iscte ・ Indegene, Inc. ・ Indego ・ Indego Africa ・ Indel ・ Indel (rural locality) ・ INDELA-I.N.SKY ・ Indeleble ・ Indelible ・ Indelible Grace ・ Indelible Ink ・ Indelible Murtceps ・ Indelible Music ・ Indelibly Stamped 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 Indefinite sum ： ウィキペディア英語版 Indefinite sum In mathematics the indefinite sum operator (also known as the antidifference operator), denoted by $\backslash sum\; \_x\; \backslash ,$ or $\backslash Delta^\; \backslash ,$,〔(On Computing Closed Forms for Indefinite Summations. Yiu-Kwong Man. J. Symbolic Computation (1993), 16, 355-376 )〕〔"If ''Y'' is a function whose first difference is the function ''y'', then ''Y'' is called an indefinite sum of ''y'' and denoted Δ−1''y''" (''Introduction to Difference Equations'' ), Samuel Goldberg〕 is the linear operator, inverse of the forward difference operator $\backslash Delta\; \backslash ,$. It relates to the forward difference operator as the indefinite integral relates to the derivative. Thus :$\backslash Delta\; \backslash sum\_x\; f(x)\; =\; f(x)\; \backslash ,\; .$ More explicitly, if $\backslash sum\_x\; f(x)\; =\; F(x)\; \backslash ,$, then :$F(x+1)\; -\; F(x)\; =\; f(x)\; \backslash ,\; .$ If ''F''(''x'') is a solution of this functional equation for a given ''f''(''x''), then so is ''F''(''x'')+''C(x)'' for any periodic function ''C(x)'' with period 1. Therefore each indefinite sum actually represents a family of functions. However the solution equal to its Newton series expansion is unique up to an additive constant C. ==Fundamental theorem of discrete calculus== Indefinite sums can be used to calculate definite sums with the formula:〔"Handbook of discrete and combinatorial mathematics", Kenneth H. Rosen, John G. Michaels, CRC Press, 1999, ISBN 0-8493-0149-1〕 :$\backslash sum\_^b\; f(k)=\backslash Delta^f(b+1)-\backslash Delta^f(a)$ 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「Indefinite sum」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.