On the representation of indefinite integrals containing Bessel functions by simple Neumann series

Indefinite integrals containing Bessel functions and their representation as simple Neumann series or alternatively in terms of Lommel's functions of two variables have been noted in the literature in connection with physical problems [1; 2; 3]. It is observed here that by a simple generalization of a result noted by Watson [4, p. 23, footnote] expressing a generating function for Bessel's function as an indefinite integral, all of the previously noted examples may be obtained as particular cases of a more general result, which is then applied to the evaluation of an integral arising in connection with noise theory. If we define