翻訳と辞書 Words near each other ・ "O" Is for Outlaw ・ "O"-Jung.Ban.Hap. ・ "Ode-to-Napoleon" hexachord ・ "Oh Yeah!" Live ・ "Our Contemporary" regional art exhibition (Leningrad, 1975) ・ "P" Is for Peril ・ "Pimpernel" Smith ・ "Polish death camp" controversy ・ "Pro knigi" ("About books") ・ "Prosopa" Greek Television Awards ・ "Pussy Cats" Starring the Walkmen ・ "Q" Is for Quarry ・ "R" Is for Ricochet ・ "R" The King (2016 film) ・ "Rags" Ragland ・ ! (album) ・ ! (disambiguation) ・ !! ・ !!! ・ !!! (album) ・ !!Destroy-Oh-Boy!! ・ !Action Pact! ・ !Arriba! La Pachanga ・ !Hero ・ !Hero (album) ・ !Kung language ・ !Oka Tokat ・ !PAUS3 ・ !T.O.O.H.! ・ !Women Art Revolution 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.