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Accessible Unlicensed Requires Authentication Published by De Gruyter December 18, 2014

Evaluation of a generalized Selberg integral

Daya K. Nagar, Sandra Milena Naranjo-Ríos and Arjun K. Gupta

Abstract

In this article, we evaluate the integral

0101xα+g-1yα+h-1(1-x)β+k-1(1-y)β+-1|x-y|2γdydx,

where α > 0, β > 0, γ ≥ 0, and g, h, k, ℓ are positive integers. Explicit expressions of the above integral are derived in simple elementary functions for various values of g, h, k, and ℓ.

MSC: 33B15; 33C20
Received: 2012-3-12
Accepted: 2014-6-9
Published Online: 2014-12-18
Published in Print: 2015-3-1

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