Derivation of modified Smyshlyaev´s formulae using integral transform of Kontorovich-Lebedev type

The aim of this work is to fill the gap between the embedding formulae for cones and the modified Smyshlyaev´s formulae. Embedding formulae for cones represent the directivity of the scattered field as multiple integrals over spatial variables. Modified Smyshlyaev´s formulae represent the same directivity as a single contour integral over parameter v. This situation resembles the convolution theorem for Fourier transform: multiple convolutions can be represented as a single integral over frequency.