New proofs of generating functions for Rogers-Szegö polynomials (Q1002307)
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scientific article; zbMATH DE number 5518806
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New proofs of generating functions for Rogers-Szegö polynomials |
scientific article; zbMATH DE number 5518806 |
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New proofs of generating functions for Rogers-Szegö polynomials (English)
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25 February 2009
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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 \textit{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 \(q \rightarrow q^{-1}\).
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Rogers-Szegö polynomials
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generating function
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\(q\)-difference operator
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\(q\)-exponential operator
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operator identity
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