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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 Mehler–Heine formula ： ウィキペディア英語版 Mehler–Heine formula In mathematics, the Mehler–Heine formula introduced by and describes the asymptotic behavior of the Legendre polynomials as the index tends to infinity, near the edges of the support of the weight. There are generalizations to other classical orthogonal polynomials, which are also called the Mehler–Heine formula. The formula complements the Darboux formulae which describe the asymptotics in the interior and outside the support. ==Legendre polynomials== The simplest case of the Mehler–Heine formula states that :$\backslash lim\; \_P\_n\backslash Bigl(\backslash cos\backslash Bigr)=J\_0(z)$ where ''P''''n'' is the Legendre polynomial of order ''n'', and ''J''0 a Bessel function. The limit is uniform over ''z'' in an arbitrary bounded domain in the complex plane. 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「Mehler–Heine formula」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.