Hyperbolic measures, moments and coefficients. Algebra on hyperbolic functions

摘要

With convolutions, we determine the Fourier transform of u(n)/[sinh(u)](n) when n is a positive integer. Studying the expansion and taking the Fourier transform of [u/[sinh(u)]](d) [u/tanh(u)](n) when n and d are strictly positive integers, we obtain some polynomials and new probability densities related to them. (C) 2008 Elsevier Inc. All rights reserved.