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Bessel functions describe the radial part of vibrations of a circular membrane.. Bessel functions, named after astronomer Friedrich Bessel who was the first to systematically study them in 1824, [1] are canonical solutions y(x) of Bessel's differential equation + + = for an arbitrary complex number, which represents the order of the Bessel function.
Download as PDF; Printable version; In other projects ... One such formula is the following integral formula involving a product of three Bessel functions:
Here the notation for Bessel functions follows the German convention, to be consistent with the original notation used by Sommerfeld. The function () is the zeroth-order Bessel function of the first kind, better known by the notation () = in English literature. This identity is known as the Sommerfeld identity.
The angular integration of an exponential in cylindrical coordinates can be written in terms of Bessel functions of the first kind [4] [5]: 113 ( ()) = and ( ()) = (). For applications of these integrals see Magnetic interaction between current loops in a simple plasma or electron gas .
Digital Library of Mathematical Functions, Equation 10.60.7, National Institute of Standards and Technology Rami Mehrem (2009), The Plane Wave Expansion, Infinite Integrals and Identities Involving Spherical Bessel Functions , arXiv : 0909.0494 , Bibcode : 2009arXiv0909.0494M
It was originally developed to compute tables of the modified Bessel function [2] but also applies to Bessel functions of the first kind and has other applications such as computation of the coefficients of Chebyshev expansions of other special functions. [3]
In mathematics, a Jackson q-Bessel function (or basic Bessel function) is one of the three q-analogs of the Bessel function introduced by Jackson (1906a, 1906b, 1905a, 1905b). The third Jackson q -Bessel function is the same as the Hahn–Exton q -Bessel function .
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