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 Jν(kr). 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 Fν 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.
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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 Jν(kr). 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 Fν 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.
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Die Hankel-Transformation ist ...... rrektur von Abbildungsfehlern.
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Em matemática, a transformada ...... transformada de Hankel (ver ).
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En mathématiques, la transform ...... me de coordonnées circulaires.
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In matematica, la trasformata ...... urier su un intervallo finito.
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In mathematics, the Hankel tra ...... series over a finite interval.
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В математике, преобразование Х ...... реобразование Бесселя — Фурье.
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ハンケル変換 (Hankel transform) とは、連 ...... 、ハンケル変換とフーリエ・ベッセル変換の間にもあると言える。
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汉克尔变换是指对任何给定函数 以第一类贝塞尔函数 作无穷级数 ...... 德国数学家 赫尔曼·汉克尔提出，又被称为傅立叶-贝塞尔变换。
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Die Hankel-Transformation ist ...... rrektur von Abbildungsfehlern.
@de
Em matemática, a transformada ...... plo, em duas dimensões, faz-se
@pt
En mathématiques, la transform ...... e k, constitue la transformée.
@fr
In matematica, la trasformata ...... urier su un intervallo finito.
@it
In mathematics, the Hankel tra ...... series over a finite interval.
@en
В математике, преобразование Х ...... реобразование Бесселя — Фурье.
@ru
ハンケル変換 (Hankel transform) とは、連 ...... 、ハンケル変換とフーリエ・ベッセル変換の間にもあると言える。
@ja
汉克尔变换是指对任何给定函数 以第一类贝塞尔函数 作无穷级数 ...... 德国数学家 赫尔曼·汉克尔提出，又被称为傅立叶-贝塞尔变换。
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label
Hankel transform
@en
Hankel-Transformation
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Hankel变换
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Transformada de Hankel
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Transformation de Hankel
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Trasformata di Hankel
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Преобразование Ханкеля
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ハンケル変換
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