We consider integrals of products of Bessel functions and of spherical Bessel functions, combined with a Gaussian factor guaranteeing convergence at infinity. Explicit representations are obtained for the integrals, building on those in the 1992 paper by McPhedran, Dawes and Scott. Attention is paid to those sums with a distributive part arising as the Gaussian tends towards a constant. Taking this limit provides explicit analytic formulae for integrals which are difficult to evaluate… Expand

Applicable Algebra in Engineering, Communication and Computing

2005

TLDR

This work reduces the integral of √kK, whereη, K, k andb are all positive real numbers, to a linear combination of two integrals, which can be expressed as a difference of two Shkarofsky functions, or evaluated numerically.Expand

The known properties of plasma dispersion functions (PDF’s) for waves in weakly relativistic, magnetized, thermal plasmas are reviewed and a large number of new results are presented. The PDF’s… Expand

THE memoir in which Bessel, the astronomer, examined in detail the functions which now bear his name was published in 1824, and was the outcome of his earlier researches concerning the expression of… Expand

Discrete spectrum continuous spectrum analytic properties of the wave function the green's function and perturbation theory quasi-classical approximation exact solutions of certain non-stationary… Expand

This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators and is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun.Expand