On a family of integrals that extend the Askey–Wilson integral

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 integra...

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Veröffentlicht in:Journal of mathematical analysis and applications Jg. 421; H. 2; S. 1101 - 1130
Hauptverfasser: Ito, Masahiko, Witte, N.S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.01.2015
Schlagworte:
Askey–Wilson polynomials
Basic hypergeometric integrals
Divided difference operators
Non-uniform lattices
Orthogonal polynomials
Semi-classical weights
Divided difference operators
Basic hypergeometric integrals
Non-uniform lattices
Semi-classical weights
Askey–Wilson polynomials
Orthogonal polynomials
ISSN:0022-247X, 1096-0813
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Zusammenfassung: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 φ2N+12N+2 basic hypergeometric functions.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2014.07.056