翻訳と辞書 Words near each other ・ Jacques Thomassen ・ Jacques Thubé ・ Jacques Thuillier ・ Jacques Thuriaux ・ Jacques Thébault ・ Jacques Tichelaar ・ Jacques Tillier ・ Jacques Tiné ・ Jacques Tioye ・ Jacques Tits ・ Jacques Tixier ・ Jacques Toja ・ Jacques Torczyner ・ Jacques Torres ・ Jacques Toubon ・ Jacques Touchard ・ Jacques Touchet ・ Jacques Tourangeau ・ Jacques Tourneur ・ Jacques Tremblay ・ Jacques Tremblay (MNA 1985) ・ Jacques Triger ・ Jacques Trudel ・ Jacques Trullier, dit Lacombe ・ Jacques Trémollet de Villers ・ Jacques Tuyisenge ・ Jacques Tétreault ・ Jacques Urbain ・ Jacques Urlus ・ Jacques Vaché 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 Jacques Touchard ： ウィキペディア英語版 Jacques Touchard Jacques Touchard (1885 – 1968) was a French mathematician. In 1953, he proved that an odd perfect number must be of the form 12''k'' + 1 or 36''k'' + 9. In combinatorics and probability theory, he introduced the Touchard polynomials. He is also known for his solution to the ménage problem of counting seating arrangements in which men and women alternate and are not seated next to their spouses. ==Touchard's Catalan identity== The following algebraic identity involving the Catalan numbers :$C\_k\; =\; =\backslash sum\_\; 2^\; C\_k.\; \backslash ,$ Using the generating function :$C(t)=\backslash sum\_\; C\_n\; t^n\; =\backslash over\; \}$ it can be proved by algebraic manipulations of generating series that Touchard's identity is equivalent to the functional equation :$\backslash right)\; =\; C(t)-1$ satisfied by the Catalan generating series ''C''(''t''). 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「Jacques Touchard」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.