翻訳と辞書 Words near each other ・ Batella ・ Batella (Lymantriidae) ・ Batelov ・ Batelusia ・ Batem ・ Bateman ・ Bateman 365 ・ Bateman baronets ・ Bateman Equation ・ Bateman function ・ Bateman Hardware ・ Bateman Hotel (Lowville, New York) ・ Bateman Island ・ Bateman Manuscript Project ・ Bateman Park ・ Bateman polynomials ・ Bateman Pulsed Column ・ Bateman transform ・ Bateman's ・ Bateman's 'Great Landowners' (1883) ・ Bateman's principle ・ Bateman, Saskatchewan ・ Bateman, Texas ・ Bateman, Western Australia ・ Bateman, Wisconsin ・ Bateman-Griffith House ・ Batemannia ・ Batemans Bay ・ Batemans Bay (New South Wales) ・ Batemans Bay High School 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 Bateman polynomials ： ウィキペディア英語版 Bateman polynomials In mathematics, the Bateman polynomials are a family ''F''''n'' of orthogonal polynomials introduced by . The Bateman–Pasternack polynomials are a generalization introduced by . Bateman polynomials are given by :$F\_n\backslash left(\backslash frac\backslash right)\backslash cosh^(x)\; =\; \backslash cosh^(x)P\_n(\backslash tanh(x))$ =\right)\cosh^(x) = \cosh^(x)P_n(\tanh(x)) showed that the polynomials ''Q''''n'' studied by , see Touchard polynomials, are the same as Bateman polynomials up to a change of variable: more precisely :$Q\_n(x)=(-1)^n2^nn!\backslash binom^F\_n(2x+1)$ Bateman and Pasternack's polynomials are special cases of the symmetric continuous Hahn polynomials. ==Examples== The polynomials of small ''n'' read :$F\_0(x)=1$; :$F\_1(x)=-x$; :$F\_2(x)=\backslash frac+\backslash fracx^2$; :$F\_3(x)=-\backslash fracx-\backslash fracx^3$; :$F\_4(x)=\backslash frac+\backslash fracx^2+\backslash fracx^4$; :$F\_5(x)=\backslash fracx-\backslash fracx^3-\backslash fracx^5$; 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「Bateman 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.