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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 Petkovšek's algorithm ： ウィキペディア英語版 Petkovšek's algorithm Petkovšek's algorithm is a computer algebra algorithm that computes a basis of hypergeometric terms solution of its input linear recurrence equation with polynomial coefficients. Equivalently, it computes a first order right factor of linear difference operators with polynomial coefficients. This algorithm is implemented in all the major computer algebra systems. == Examples == * Given the linear recurrence :$4(n+2)(2n+3)(2n+5)a(n+2)$ -12(2n+3)(9n^2+27n+22)a(n+1) +81(n+1)( 3n+2)(3n+4) a(n) =0, the algorithm finds two linearly independent hypergeometric terms that are solution: :$\backslash left(\; \}\; \backslash right)\; ^\},\backslash qquad\; \backslash left(\; \}\; \backslash right)\; ^\}.$ (Here, $\backslash Gamma$ denotes Euler's Gamma function.) Note that the second solution is also a binomial coefficient $\backslash binom$, but it is not the aim of this algorithm to produce binomial expressions. * Given the sum :$a(n)=\backslash sum\_^n^2\backslash binom^2\},$ coming from Apéry's proof of the irrationality of $\backslash zeta(3)$, Zeilberger's algorithm computes the linear recurrence :$(n+2)^3a(n+2)-(17n^2+51n+39)(2n+3)a(n+1)+(n+1)^3a(n)=0.$ Given this recurrence, the algorithm does not return any hypergeometric solution, which proves that $a(n)$ does not simplify to a hypergeometric term. 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「Petkovšek's algorithm」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.