A General Inversion Pair and p-deformation of Askey Scheme

Abstract

The present work incorporates the general inverse series relations involving p -Pochhammer symbol and p -Gamma function. A general class of p-polynomials is introduced by means of this general inverse pair which is used to derive the generating function relations and summation formulas for certain p -polynomials belonging to this general class. This includes the p -deformation of Jacobi polynomials, the Brafman polynomials and Konhauser polynomials. Moreover, the orthogonal polynomials of Racah and those of Wilson are also provided p-deformation by means of the general inversion pair. The generating function relations and summation formulas for these polynomials are also derived. We then emphasize on the combinatorial identities and obtain their p-deformed versions.