p-Deformation of a General Class of Polynomials and its Properties

Abstract

The work incorporates the extension of the Srivastava-Pathan’s generalized polynomial by means of p-generalized gamma function: Γ<sub>p</sub> and Pochhammer p-symbol (x)<sub>n,p</sub> due to Rafael Dıaz and Eddy Pariguan [Divulgaciones Mathematicas Vol.15, No. 2(2007), pp. 179-192]. We establish the inverse series relation of this extended polynomial with the aid of general inversion theorem. We also obtain the generating function relations and the differential equation. Certain <em>p</em>-deformed combinatorial identities are illustrated in the last section.