Evaluation of a Class of Multiple Integrals

Abstract

In his paper [1], K. L. D. Gunawardena introduced two sequences of multiple integrals (see (1.1) and (1.2) below) encountered in one of his courses of mathematical statistics. Using a key probability result, he evaluated these integrals. At the end of [1], he asked the question whether these integrals could be computed without using results from probability theory. The aim of this paper is to answer that question and make direct computations of these integrals by elementary methods without using probabilistic tools.