Discrete analogues of Macdonald-Mehta integrals

@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

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