On a Family of Integrals that extend the Askey-Wilson Integral
M. Ito, N.S. Witte

TL;DR
This paper introduces a family of integrals extending the Askey-Wilson integral, characterizing them via $q$-difference equations and expressing their evaluations through hypergeometric functions and Jackson integrals.
Contribution
It generalizes the Askey-Wilson integral to higher N, providing new $q$-difference equations and explicit evaluation formulas.
Findings
Integrals are characterized by $(N-1)$-th order linear $q$-difference equations.
Explicit evaluation as finite sums of Jackson integrals or hypergeometric functions.
Extension of the Askey-Wilson integral family to arbitrary N.
Abstract
We study a family of integrals parameterised by generalising the Askey-Wilson integral which has arisen in the theory of -analogs of monodromy preserving deformations of linear differential systems and in theory of the Baxter operator for the open quantum spin chain. These integrals are particular examples of moments defined by weights generalising the Askey-Wilson weight and we show the integrals are characterised by various -th order linear -difference equations which we construct. In addition we demonstrate that these integrals can be evaluated as a finite sum of -type Jackson integrals or basic hypergeometric functions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Mathematical functions and polynomials
