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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 Askey–Wilson polynomial ： ウィキペディア英語版 Askey–Wilson polynomials In mathematics, the Askey–Wilson polynomials (or ''q''-Wilson polynomials) are a family of orthogonal polynomials introduced by as q-analogs of the Wilson polynomials. They include many of the other orthogonal polynomials in 1 variable as special or limiting cases, described in the Askey scheme. Askey–Wilson polynomials are the special case of Macdonald polynomials (or Koornwinder polynomials) for the non-reduced affine root system of type (''C'', ''C''1), and their 4 parameters ''a'', ''b'', ''c'', ''d'' correspond to the 4 orbits of roots of this root system. They are defined by :$p\_n(x;a,b,c,d|q)\; =$ (ab,ac,ad;q)_na^\;_\phi_3 \left( q^&abcdq^&ae^&ae^ \\ ab&ac&ad \end ; q,q \right ) where φ is a basic hypergeometric function and ''x'' = cos(θ) and (,,,)''n'' is the q-Pochhammer symbol. Askey–Wilson functions are a generalization to non-integral values of ''n''. ==See also== *Askey scheme 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「Askey–Wilson 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.