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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 sieved ultraspherical polynomials ： ウィキペディア英語版 sieved ultraspherical polynomials In mathematics, the two families ''c''(''x'';''k'') and ''B''(''x'';''k'') of sieved ultraspherical polynomials, introduced by Waleed Al-Salam, W.R. Allaway and Richard Askey in 1984, are the archetypal examples of sieved orthogonal polynomials. Their recurrence relations are a modified (or "sieved") version of the recurrence relations for ultraspherical polynomials. ==Recurrence relations== For the sieved ultraspherical polynomials of the first kind the recurrence relations are :$2xc\_n^\backslash lambda(x;k)\; =\; c\_^\backslash lambda(x;k)\; +\; c\_^\backslash lambda(x;k)$ if ''n'' is not divisible by ''k'' :$2x(m+\backslash lambda)c\_^\backslash lambda(x;k)\; =\; (m+2\backslash lambda)c\_^\backslash lambda(x;k)\; +\; mc\_^\backslash lambda(x;k)$ For the sieved ultraspherical polynomials of the second kind the recurrence relations are :$2xB\_^\backslash lambda(x;k)\; =\; B\_^\backslash lambda(x;k)\; +\; B\_^\backslash lambda(x;k)$ if ''n'' is not divisible by ''k'' :$2x(m+\backslash lambda)B\_^\backslash lambda(x;k)\; =\; mB\_^\backslash lambda(x;k)\; +(m+2\backslash lambda)B\_^\backslash lambda(x;k)$ 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「sieved ultraspherical polynomials」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.