Abstract
AbstractCertain 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) concernswhere 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.
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More From: The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
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