## Missouri Journal of Mathematical Sciences

- Missouri J. Math. Sci.
- Volume 17, Issue 3 (2005), 148-152.

### 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.

#### Article information

**Source**

Missouri J. Math. Sci., Volume 17, Issue 3 (2005), 148-152.

**Dates**

First available in Project Euclid: 22 August 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.mjms/1566439478

**Digital Object Identifier**

doi:10.35834/2005/1703148

**Zentralblatt MATH identifier**

1097.26011

**Subjects**

Primary: 26B10: Implicit function theorems, Jacobians, transformations with several variables

Secondary: 26B15: Integration: length, area, volume [See also 28A75, 51M25] 26B20: Integral formulas (Stokes, Gauss, Green, etc.) 28A35: Measures and integrals in product spaces

#### Citation

Akkouchi, Mohamed. Evaluation of a Class of Multiple Integrals. Missouri J. Math. Sci. 17 (2005), no. 3, 148--152. doi:10.35834/2005/1703148. https://projecteuclid.org/euclid.mjms/1566439478