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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 Whittaker function ： ウィキペディア英語版 Whittaker function In mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by to make the formulas involving the solutions more symmetric. More generally, introduced Whittaker functions of reductive groups over local fields, where the functions studied by Whittaker are essentially the case where the local field is the real numbers and the group is SL2(R). Whittaker's equation is :$\backslash frac+\backslash left(-\backslash frac+\backslash frac+\backslash frac\backslash right)w=0.$ It has a regular singular point at 0 and an irregular singular point at ∞. Two solutions are given by the Whittaker functions ''M''κ,μ(''z''), ''W''κ,μ(''z''), defined in terms of Kummer's confluent hypergeometric functions ''M'' and ''U'' by :$M\_\backslash left(z\backslash right)\; =\; \backslash exp\backslash left(-z/2\backslash right)z^\}M\backslash left(\backslash mu-\backslash kappa+\backslash frac,\; 1+2\backslash mu;\; z\backslash right)$ :$W\_\backslash left(z\backslash right)\; =\; \backslash exp\backslash left(-z/2\backslash right)z^\}U\backslash left(\backslash mu-\backslash kappa+\backslash frac,\; 1+2\backslash mu;\; z\backslash right).$ Whittaker functions appear as coefficients of certain representations of the group SL2(R), called Whittaker models. ==References== * *. *. * * * * *. *. * 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「Whittaker 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.