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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 Kontorovich–Lebedev transform ： ウィキペディア英語版 Kontorovich–Lebedev transform In mathematics, the Kontorovich–Lebedev transform is an integral transform which uses a Macdonald function (modified Bessel function of the second kind) with imaginary index as its kernel. Unlike other Bessel function transforms, such as the Hankel transform, this transform involves integrating over the index of the function rather than its argument. The transform of a function ''ƒ''(''x'') and its inverse (provided they exist) are given below: :$g(y)\; =\; \backslash int\_0^\backslash infty\; f(x)\; K\_(x)\; \backslash ,\; dx$ :$f(x)\; =\; \backslash frac\; \backslash int\_0^\backslash infty\; g(y)\; K\_(x)\; \backslash sinh\; (\backslash pi\; y)\; y\; \backslash ,\; dy\; .$ Laguerre previously studied a similar transform regarding Laguerre function as: :$g(y)\; =\; \backslash int\_0^\backslash infty\; f(x)e^\; L\_(x)\; \backslash ,\; dx$ :$f(x)\; =\; \backslash int\_0^\backslash infty\; \backslash frac\; L\_y(x)\; \backslash ,\; dy.$ Erdélyi ''et al.'', for instance, contains a short list of Kontorovich–Lebedev transforms as well references to the original work of Kontorovich and Lebedev in the late 1930s. This transform is mostly used in solving the Laplace equation in cylindrical coordinates for wedge shaped domains by the method of separation of variables. == References == * Erdélyi ''et al.'' ''Table of Integral Transforms Vol. 2'' (McGraw Hill 1954) * I.N. Sneddon, ''The use of integral Transforms'', (McGraw Hill, New York 1972) * 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「Kontorovich–Lebedev transform」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.