Some Basic Hypergeometric Extensions of Integrals of Selberg and Andrews

Abstract

A. Selberg evaluated an important multivariable extension of the beta function integral. Andrews found a related integral and evaluated it using a result of Dyson, Gunson and Wilson. Basic hypergeometric, or q-series, extensions of these integrals are considered and evaluated in the two-dimensional case. Conjectures are given for the values of these integrals in the n-dimensional case.