Connections between generalized singular functions and Bessel functions

Abstract

After having introduced a suitable extension of the concept of «generalized singular function», a somewhat detailed mathematical investigation of the structure of the integrals involved is made. Among the main results, various integral relationships are obtained, which show the intimate connection between generalized singular functions and Bessel functions. A further elaboration of our formulae, leading to some new multiple integrals involving Bessel functions, will be given in a subsequent paper.