Editing Hankel transform (section)

{{Short description|Mathematical operation}}
{{Distinguish|Hankel matrix transform}}

In [[mathematics]], the '''Hankel transform''' expresses any given function ''f''(''r'') as the weighted sum of an infinite number of [[Bessel functions|Bessel functions of the first kind]] {{math|''J<sub>ν</sub>''(''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 {{math|''F<sub>ν</sub>''}} 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.