Calculation of some integrals involving the Macdonald function by using Fourier transform

Abstract

By using the convolution theorem of the Fourier transform (Faltung theorem), the following integral involving the Macdonald function is calculated, ∫−∞∞|t′|α+2nKα(a|t′|)|t−t′|β+2mKβ(a|t−t′|)dt′. As a consistency test of the result obtained, setting the parameters α, β, m, n, t and a to particular values, some integrals reported in the literature are recovered. It turns out that the calculation method of integrals via the convolution theorem is useful for calculating other infinite integrals involving the Macdonald function.