Generalized q-Difference Equation for Generalized Cigler's Polynomials
Generalized q-Difference Equation
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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