Transcription of Bessel Functions and Their Applications
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Bessel Functions and Their Applications
Bessel Functions and Their ApplicationsJennifer Niedziela University of Tennessee - Knoxville(Dated: October 29, 2008) Bessel Functions are a series of solutions to a second order differential equation that arise inmany diverse situations. This paper derives the Bessel Functions through use of a series solutionto a differential equation, develops the different kinds of Bessel Functions , and explores the topicof zeroes. Finally, Bessel Functions are found to be the solution to the Schroedinger equation in asituation with cylindrical special types of what would later be known asBessel Functions were studied by Euler, Lagrange, andthe Bernoullis, the Bessel Functions were first used by Bessel to describe three body motion, with the Besselfunctions appearing in the series expansion on planetaryperturbation [1].
Oct 29, 2008 · constants to be determined via application of the bound-ary conditions. As the solution must be nite at x= 0, and as N m(kr) !1as x!0, this means that the coef- cient of N m(kr) = B= 0, leaving R(r) to be expressed: R(r) = AJ m(kr) (25) Using the boundary condition that = 0 at the radius of the disk, we have the condition that J m(kr b) = 0, which
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