Title 
Utility of integral representations for basic hypergeometric functions and orthogonal polynomials 
Authors 
Cohl, Howard S. , COSTAS SANTOS, ROBERTO SANTIAGO 
External publication 
Si 
Means 
Ramanujan J. 
Scope 
Article 
Nature 
Científica 
JCR Quartile 
3 
SJR Quartile 
2 
JCR Impact 
0.70000 
SJR Impact 
0.55900 
Web 
https://www.scopus.com/inward/record.uri?eid=2s2.085132548888&doi=10.1007%2fs11139021005095&partnerID=40&md5=8fce344953c9af4a43568a803850a122 
Publication date 
23/06/2022 
ISI 
000814913900001 
Scopus Id 
2s2.085132548888 
DOI 
10.1007/s11139021005095 
Abstract 
We describe the utility of integral representations for sums of basic hypergeometric functions. In particular we use these to derive an infinite sequence of transformations for symmetrizations over certain variables which the functions possess. These integral representations were studied by Bailey, Slater, Askey, Roy, Gasper and Rahman and were also used to facilitate the computation of certain outstanding problems in the theory of basic hypergeometric orthogonal polynomials in the qAskey scheme. We also generalize and give consequences and transformation formulas for some fundamental integrals connected to nonterminating basic hypergeometric series and the AskeyWilson polynomials. We express a certain integral of a ratio of infinite qshifted factorials as a symmetric sum of two basic hypergeometric series with argument q. The result is then expressed as a qintegral. Examples of integral representations applied to the derivation of generating functions for the AskeyWilson polynomials are given and as well the computation of a missing generating function for the continuous dual qHahn polynomials. 
Keywords 
Basic hypergeometric functions; Transformations; Integral representations; Basic hypergeometric orthogonal polynomials; Generating functions 
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