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

By using the convolution theorem of the Fourier transform (Faltung theorem), the following integral involving the Macdonald function is calculated, integral(infinity)(-infinity) vertical bar t'vertical bar alpha+2n x K-alpha(alpha vertical bar t'vertical bar)vertical bar t - t'vertical bar(beta+2m) K-beta(alpha vertical bar t - t'vertical bar)dt'. As a consistency test of the result obtained, setting the parameters alpha, beta, 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. (C) 2016 Elsevier Inc. All rights reserved.