@article{Brent2016DiscreteAO,
title={Discrete analogues of Macdonald-Mehta integrals},
author={Richard P. Brent and Christian Krattenthaler and Ole Warnaar},
journal={J. Comb. Theory, Ser. A},
year={2016},
volume={144},
pages={80-138}
}

We consider identities satisfied by discrete analogues of Mehta-like integrals. The integrals are related to Selberg’s integral and the Macdonald conjectures. Our discrete analogues have the form Sα,β,δ(r, n) := ∑ k1,...,kr∈Z ∏ 1≤i<j≤r |kα i − kα j |β ∏r j=1 |kj| ( 2n n+kj ) where α, β, δ, r, n are non-negative integers subject to certain restrictions. In the ten cases that we consider, it is possible to express Sα,β,δ(r, n) as a product of Gamma functions and simple functions such as powers of… CONTINUE READING

A First Course, Graduate Texts in Math., vol. 129, Springer-Verlag, New York, 1991. R.P. Brent et al. / Journal of Combinatorial Theory, Series A 144 • 2016