Certain Integral Transforms and Their Applications in Propagation of Laguerre-Gaussian Schell-model Beams

Abstract

The principal aim of the present work is to investigate a new class of integral transforms involving the product of Bessel function of the first kind of arbitrary order with generalized Laguerre polynomials and logarithmic functions which deduce some new results in terms of the digamma function and Kamp´e de F´eriet functions. A novel expression is found for the Kamp´e de F´eriet function F1:2;1 2:1;0 in terms of hypergeometric functions 1F1, 2F2 and 3F2. Finally, The results obtained are applied in the problem of propagation of Laguerre-Bessel-Gaussian Schell-model beams as an application.