2014/05/15 by Masahiko Ito, Ito, M., N. S. Witte +1
Mathematics · Physics and Astronomy · #05E35 #33C45 #33D15 #33D60 #39A05 #42A52 #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1405.3723
openalex publication_date 2014/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a family of integrals parameterised by N = 2,3,… generalising the Askey-Wilson integral N=2 which has arisen in the theory of q-analogs of monodromy preserving deformations of linear differential systems and in theory of the Baxter Q operator for the XXZ 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 (N-1) -th order linear q-difference equations which we construct. In addition we demonstrate that these integrals can be evaluated as a finite sum of (N-1) BC1 -type Jackson integrals or 2N+2φ2N+1 basic hypergeometric functions.