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Non-classical integrals of Bessel functions

Published online by Cambridge University Press:  17 February 2009

S. N. Stuart
S. N. Stuart
Affiliation:
C.S.I.R.O. Division of Chemical Physics, P. O. Box 160, Clayton, Victoria 3168
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Abstract

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Certain definite integrals involving spherical Bessel functions are treated by relating them to Fourier integrals of the point multipoles of potential theory. The main result (apparently new) concerns

where l1, l2 and N are non-negative integers, and r1 and r2 are real; it is interpreted as a generalized function derived by differential operations from the delta function δ(r1 − r2). An ancillary theorem is presented which expresses the gradient ∇2nYlm(∇) of a spherical harmonic function g(r)YLM(Ω) in a form that separates angular and radial variables. A simple means of translating such a function is also derived.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 3 , January 1981 , pp. 368 - 378
Copyright
Copyright © Australian Mathematical Society 1981

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