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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 Stieltjes–Wigert polynomials ： ウィキペディア英語版 Stieltjes–Wigert polynomials In mathematics, Stieltjes–Wigert polynomials (named after Thomas Jan Stieltjes and Carl Severin Wigert) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, for the weight function 〔Up to a constant factor this is ''w''(''q''−1/2''x'') for the weight function ''w'' in Szegő (1975), Section 2.7. See also Koornwinder et al. (2010), Section 18.27(vi).〕 :$w(x)\; =\; \backslash frac\; \backslash exp(-k^2\backslash log^2\; x)$ on the positive real line ''x'' > 0. The moment problem for the Stieltjes–Wigert polynomials is indeterminate; in other words, there are many other measures giving the same family of orthogonal polynomials (see Krein's condition). Koekoek et al. (2010) give in Section 14.27 a detailed list of the properties of these polynomials. ==Definition== The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by〔Up to a constant factor ''S''''n''(''x'';''q'')=''p''''n''(''q''−1/2''x'') for ''p''''n''(''x'') in Szegő (1975), Section 2.7.〕 :$\backslash displaystyle\; S\_n(x;q)\; =\; \backslash fracx)$ (where ''q'' = ''e''). 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「Stieltjes–Wigert 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.