COMPUTATION OF INTEGRALS OVER THE HALF-LINE INVOLVING PRODUCTS OF BESSEL-FUNCTIONS, WITH APPLICATION TO MICROWAVE TRANSMISSION-LINES

We consider the numerical computation of integrals of the form (0) int egral(infinity) f(x)J(nu)(ax)J(mu)(bx)dx. Integrals of this type occur , e.g., in the analysis of planar transmission lines in microwave appl ications when using the Spectral-Domain Galerkin-Method, where the com putations are done in the Fourier transform or spectral domain. If f i s only slowly decaying, then these integrals cannot be efficiently com puted by standard methods, because of the irregular oscillating mature of the integrand. The method developed here is to replace the Bessel functions by asymptotic expansions, then to change the path of integra tion into the complex plane, and apply the Gauss-laguerre quadrature f ormula. Proceeding in this way, we need only a very small number of fu nction values of f to compute the integral to high accuracy.