This paper applies He's homotopy perturbation method to compute a large variety of integral transforms. As illustration, the paper gives special attention to the Esscher transform, the Fourier transform, the Hankel transform, the Mellin transform, the Stieljes transform and some applications.

It is shown that matrix quotients of submatrices of a spherical matrix are distributed as matrix Cauchy. This generalizes known results for scalar ratios of independent normal variates. The derivations are simple and make use of the theory of invariant measures on manifolds.