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Download as PDF; Printable version; In other projects ... One such formula is the following integral formula involving a product of three Bessel functions:
Bessel functions describe the radial part of vibrations of a circular membrane.. Bessel functions, first defined by the mathematician Daniel Bernoulli [1] [failed verification] and then generalized by Friedrich Bessel, [citation needed] 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; ... The incomplete Bessel functions are defined as the same delay ... defines the integral bound of the upper-incomplete form ...
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 .
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