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- Hankel_transform abstract "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.More precisely, the Hankel transform of order ν of a function f(r) is given by:where Jν is the Bessel function of the first kind of order ν with ν ≥ − 1/2. The inverse Hankel transform of Fν(k) is defined as:which can be readily verified using the orthogonality relationship described below. 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.".
- Hankel_transform wikiPageExternalLink hankelrevi.pdf.
- Hankel_transform wikiPageExternalLink abstract.cfm?URI=oe-10-12-521.
- Hankel_transform wikiPageID "1452960".
- Hankel_transform wikiPageRevisionID "606152297".
- Hankel_transform hasPhotoCollection Hankel_transform.
- Hankel_transform subject Category:Integral_transforms.
- Hankel_transform comment "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.".
- Hankel_transform label "Hankel transform".
- Hankel_transform label "Hankel-Transformation".
- Hankel_transform label "Hankel变换".
- Hankel_transform label "Transformada de Hankel".
- Hankel_transform label "Преобразование Ханкеля".
- Hankel_transform label "ハンケル変換".
- Hankel_transform sameAs Hankel-Transformation.
- Hankel_transform sameAs Transformation_de_Hankel.
- Hankel_transform sameAs ハンケル変換.
- Hankel_transform sameAs Transformada_de_Hankel.
- Hankel_transform sameAs m.052s0h.
- Hankel_transform sameAs Q155208.
- Hankel_transform sameAs Q155208.
- Hankel_transform wasDerivedFrom Hankel_transform?oldid=606152297.
- Hankel_transform isPrimaryTopicOf Hankel_transform.