翻訳と辞書 Words near each other ・ Ramanuja Vijayaraghavan ・ Ramanujacharya (film) ・ Ramanujam vanishing theorem ・ Ramanujam Varatharaja Perumal ・ Ramanujam–Samuel theorem ・ Ramanujan (disambiguation) ・ Ramanujan (film) ・ Ramanujan graph ・ Ramanujan Institute for Advanced Study in Mathematics ・ Ramanujan IT City ・ Ramanujan Mathematical Society ・ Ramanujan prime ・ Ramanujan Prize ・ Ramanujan summation ・ Ramanujan tau function ・ Ramanujan theta function ・ Ramanujan's congruences ・ Ramanujan's lost notebook ・ Ramanujan's master theorem ・ Ramanujan's sum ・ Ramanujan's ternary quadratic form ・ Ramanujan–Nagell equation ・ Ramanujan–Petersson conjecture ・ Ramanujan–Sato series ・ Ramanujan–Soldner constant ・ Ramanujapur ・ Ramanujapuram, Thanjavur ・ Ramanujar (TV series) ・ Ramanujganj ・ Ramapala 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 Ramanujan theta function ： ウィキペディア英語版 Ramanujan theta function In mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties. In particular, the Jacobi triple product takes on a particularly elegant form when written in terms of the Ramanujan theta. The function is named after Srinivasa Ramanujan. ==Definition== The Ramanujan theta function is defined as :$f(a,b)\; =\; \backslash sum\_^\backslash infty$ a^ \; b^ for |''ab''| < 1. The Jacobi triple product identity then takes the form :$f(a,b)\; =\; (-a;\; ab)\_\backslash infty\; \backslash ;(-b;\; ab)\_\backslash infty\; \backslash ;(ab;ab)\_\backslash infty.$ Here, the expression $(a;q)\_n$ denotes the q-Pochhammer symbol. Identities that follow from this include :$f(q,q)\; =\; \backslash sum\_^\backslash infty\; q^\; =$ and :$f(q,q^3)\; =\; \backslash sum\_^\backslash infty\; q^\; =$ and :$f(-q,-q^2)\; =\; \backslash sum\_^\backslash infty\; (-1)^n\; q^\; =$ (q;q)_\infty this last being the Euler function, which is closely related to the Dedekind eta function. The Jacobi theta function may be written in terms of the Ramanujan theta function as: :$\backslash vartheta(w,\; q)=f(qw^2,qw^)$ 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「Ramanujan theta function」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.