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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 Hankel transform ： ウィキペディア英語版 Hankel transform In mathematics, the Hankel transform expresses any given function ''f''(''r'') as the weighted sum of an infinite number of Bessel functions of the first kind . The Bessel functions in the sum are all of the same order ν, but differ in a scaling factor ''k'' along the ''r''-axis. The necessary coefficient of each Bessel function in the sum, as a function of the scaling factor ''k'' constitutes the transformed function. The Hankel transform is an integral transform and was first developed by the mathematician Hermann Hankel. It is also known as the Fourier–Bessel transform. Just as the Fourier transform for an infinite interval is related to the Fourier series over a finite interval, so the Hankel transform over an infinite interval is related to the Fourier–Bessel series over a finite interval. ==Definition== The Hankel transform of order ν of a function ''f''(''r'') is given by: :$F\_\backslash nu(k)\; =\; \backslash int\_0^\backslash infty\; f(r)J\_\backslash nu(kr)\backslash ,r\backslash operatorname\backslash !r$ where $J\_\backslash nu$ is the Bessel function of the first kind of order $\backslash nu$ with $\backslash nu\backslash geq\; -\backslash frac$ The inverse Hankel transform of is defined as: :$f(r)\; =\backslash int\_0^\backslash infty\; F\_\backslash nu(k)J\_\backslash nu(kr)\; k\backslash operatorname\backslash !k$ which can be readily verified using the orthogonality relationship described below. 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「Hankel 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.