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arXiv · 2606.01140

$q$-Selberg extensions of Gasper's two stage $q$-beta integrals

Masahiko Ito·Peter J. Forrester
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Abstract

Gasper gave a two-step extension of the Askey-Roy formula for a beta-integral type defined on the unit circle. This involved increasing the number of parameters and adding a balancing condition. We derive a multidimensional generalization of the final formula in Gasper's extension. By considering a two-step degeneration involving parameters our generalization becomes Tarasov-Varchenko's formula -- itself a multidimensional generalization of the original Askey-Roy formula. The proof is done by Aomoto's method. This generalized integration by parts strategy makes use of a class of functions known as the fundamental invariants of type $BC$.

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Masahiko Ito, Peter J. Forrester. 2026-05-31. $q$-Selberg extensions of Gasper's two stage $q$-beta integrals. https://arxiv.org/abs/2606.01140

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