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Zbl 0874.41012
Ikonomou, M.; Köhler, P.; Jacob, A.F.
Computation of integrals over the half-line involving products of Bessel functions, with application to microwave transmission lines. (English)
[J] Z. Angew. Math. Mech. 75, No.12, 917-926 (1995). ISSN 0044-2267; ISSN 0946-8463/e

The numerical computation of integrals of the form $\int^\infty_0 f(x)J_\nu (ax) J_\mu (bx)dx$ 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.
[C.L.Koul (Jaipur)]

MSC 2000:: *41A55 Approximate quadratures
33C20 Generalized hypergeometric series
65D30 Numerical integration

Keywords: Bessel functions; Gauss-Laguerre quadrature formula

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