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New proofs of generating functions for Rogers-Szegö polynomials. (English) Zbl 1160.33312
The author first presents the $q$-exponential operator and derived a new operator identity. Using the $q$-exponential operator new proofs of the four generating functions of Rogers-Szegő polynomials due to {\it L. Carlitz} [Collect. Math. 23, 91--104 (1972; Zbl 0273.33012)] have been given. In addition to these, four auxiliary generating functions for Rogers-Szegő polynomials are obtained by replacing $q \rightarrow q^{-1}$.

33D45Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
42C05General theory of orthogonal functions and polynomials
Full Text: DOI
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