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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 Elliptic hypergeometric series ： ウィキペディア英語版 Elliptic hypergeometric series In mathematics, an elliptic hypergeometric series is a series Σ''c''''n'' such that the ratio ''c''''n''/''c''''n''−1 is an elliptic function of ''n'', analogous to generalized hypergeometric series where the ratio is a rational function of ''n'', and basic hypergeometric series where the ratio is a periodic function of the complex number ''n''. They were introduced by in their study of elliptic 6-j symbols. For surveys of elliptic hypergeometric series see or . ==Definitions== The q-Pochhammer symbol is defined by :$\backslash displaystyle(a;q)\_n\; =\; \backslash prod\_^\; (1-aq^k)=(1-a)(1-aq)(1-aq^2)\backslash cdots(1-aq^).$ :$\backslash displaystyle(a\_1,a\_2,\backslash ldots,a\_m;q)\_n\; =\; (a\_1;q)\_n\; (a\_2;q)\_n\; \backslash ldots\; (a\_m;q)\_n.$ The modified Jacobi theta function with argument ''x'' and nome ''p'' is defined by :$\backslash displaystyle\; \backslash theta(x;p)=(x,p/x;p)\_\backslash infty$ :$\backslash displaystyle\; \backslash theta(x\_1,...,x\_m;p)=\backslash theta(x\_1;p)...\backslash theta(x\_m;p)$ The elliptic shifted factorial is defined by :$\backslash displaystyle(a;q,p)\_n\; =\; \backslash theta(a;p)\backslash theta(aq;p)...\backslash theta(aq^;p)$ :$\backslash displaystyle(a\_1,...,a\_m;q,p)\_n=(a\_1;q,p)\_n\backslash cdots(a\_m;q,p)\_n$ The theta hypergeometric series ''r''+1''E''''r'' is defined by :$\backslash displaystyle;b\_1,...,b\_r;q,p;z)\; =\; \backslash sum\_^\backslash infty\backslash fracz^n$ The very well poised theta hypergeometric series ''r''+1''V''''r'' is defined by :$\backslash displaystyle;q,p;z)\; =\; \backslash sum\_^\backslash infty\backslash frac\backslash frac(qz)^n$ The bilateral theta hypergeometric series ''r''''G''''r'' is defined by :$\backslash displaystyle;b\_1,...,b\_r;q,p;z)\; =\; \backslash sum\_^\backslash infty\backslash fracz^n$ 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「Elliptic hypergeometric series」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.