A method for computing bessel function integrals

A method for numerical calculation of integrals containing Bessel functions of integer or integer plus one-half order is described. The calculation involves first a one-dimensional Fourier sine or cosine transform followed by evaluation of the coefficient of the Chebyshev series of the Fourier-transformed function in the case of the Bessel function and evaluation of the Legendre expansion coefficient in the case of the spherical Bessel function. A generalization of the method for the computation of an integral involving the Bessel function of arbitrary real order v is presented as well.