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Computation of integrals over the half-line involving products of Bessel functions, with application to microwave transmission lines. (English) Zbl 0874.41012
The numerical computation of integrals of the form 0 f(x)J ν (ax)J μ (bx)dx is considered in this paper. The method developed here is to replace the Bessel functions by asymptotic expansions, then to change the path of integration into the complex plane and apply the Gauss-Laguerre quadrature formula. Only a small number of function values of f to compute the integral to a high degree of accuracy is required in this method.
MSC:
41A55Approximate quadratures
33C20Generalized hypergeometric series, p F q
65D30Numerical integration