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A <i>q</i>-Operational Equation for Carlitz’s <i>q</i>-Operators with Some Applications
Rogers–Szegö polynomials are the basis in the Scheme of basic hypergeometric orthogonal polynomials. By solving a <i>q</i>-operational equation with formal power series, Liu introduced a new <i>q</i>-exponential operational identity and developed a systematic method to prove the identities involving the Rogers–Szegö polynomials. In this paper, motivated by Carlitz's <i>q</i>-operators and …