A new family of q-polynomials, named generalized Cauchy and Hahn polynomials, is introduced via generalized homogeneous q-difference operators, together with generating, Mehler, and Rogers-type formulas.
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Some homogeneous $q$-difference operators and the associated generalized Hahn polynomials
A new family of q-polynomials, named generalized Cauchy and Hahn polynomials, is introduced via generalized homogeneous q-difference operators, together with generating, Mehler, and Rogers-type formulas.