On the Sonine-Bessel integral representation

Using an integral representation for the first kind Hankel (Hankel-Bessel) function we obtain the so-called Basset formula, an integral representation for the second kind modified Bessel function. Using the Sonine-Bessel integral representation we obtain the Fourier cosine integral transform of the zero order Bessel function. As an application we present the calculation of the Green's function associated with a second order partial differential equation , particularly a wave equation for a lossy two-dimensional medium. This application is associated to the transient electromagnetic field radiated by a pulsed source in the presence of dispersive media, which is of great importance in the theory of geophysical prospecting, lightning studies