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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 Sheffer sequence ： ウィキペディア英語版 Sheffer sequence In mathematics, a Sheffer sequence or poweroid is a polynomial sequence, i.e., a sequence of polynomials in which the index of each polynomial equals its degree, satisfying conditions related to the umbral calculus in combinatorics. They are named for Isador M. Sheffer. ==Definition== Fix a polynomial sequence ''p''''n''. Define a linear operator ''Q'' on polynomials in ''x'' by :$Qp\_n(x)\; =\; np\_(x)\backslash ,\; .$ This determines ''Q'' on all polynomials. The polynomial sequence ''p''''n'' is a ''Sheffer sequence'' if the linear operator ''Q'' just defined is ''shift-equivariant''. Here, we define a linear operator ''Q'' on polynomials to be ''shift-equivariant'' if, whenever ''f''(''x'') = ''g''(''x'' + ''a'') = ''T''''a'' ''g''(''x'') is a "shift" of ''g''(''x''), then (''Qf'')(''x'') = (''Qg'')(''x'' + ''a''); i.e., ''Q'' commutes with every shift operator: ''T''''a''''Q'' =''QT''''a''. Such a ''Q'' is a delta operator. 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「Sheffer sequence」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.