A p-deformed q-inverse pair and associated polynomials including Askey scheme
Commun. Korean Math. Soc.
Published online March 12, 2019
Rajesh V. Savalia
Department of Mathematical Sciences, P. D. Patel institute of Applied Sciences, CHARUSAT-Changa
Abstract : We construct a general bi-basic inverse series relation which provides extension to several q-polynomials including the Askey-Wilson polynomials and the q-Racah polynomials. We introduce a general class of polynomials suggested by this general inverse pair which would unify certain polynomials such as the q-extended Jacobi polynomials and q-Konhauser polynomials. We then emphasize on applications of the general inverse pair and obtain the generating function relations, summation formulas involving the associated polynomials and derive the p-deformation of some of the q-analogues of Riordan's classes of inverse series relations. We also illustrate the companion matrix corresponding to the general class of polynomials; this is followed by a chart showing the reducibility of the extended p-deformed Askey-Wilson polynomials as well as the extended p-deformed q-Racah polynomials.
Keywords : q,p-Gamma function, q,p-Pochhammer symbol, p-Deformed q-polynomial, q-Inverse series
MSC numbers : 33D15, 33D45, 33D65
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