Generalized q-difference equation for generalized Cigler's polynomials

Samaher A. Abdul-Ghani; Husam L. Saad

doi:10.5269/bspm.77414

Samaher A. Abdul-Ghani
Husam L. Saad University of Basrah

Abstract

This work establishes the generalized Cigler's polynomials and the generalized homogeneous q-shift operator. The q-difference equation is then utilized to demonstrate numerous polynomial q-identities, including the generating function and its extension, Rogers' formula and its extension, and Mehler's formula and its extension for the generalized Cigler's polynomials. Also presented a transformational identity involving generating functions for generalized Cigler's polynomials.

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