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• W3100331121 abstract "We present an operator approach to Rogers-type formulas and Mehler’s formula for the Al-Salam–Carlitz polynomials Un(x,y,a;q). By using the q-exponential operator, we obtain a Rogers-type formula, which leads to a linearization formula. With the aid of a bivariate augmentation operator, we get a simple derivation of Mehler’s formula due to Al-Salam and Carlitz [“Some orthogonal q-polynomials,” Math. Nachr. 30, 47 (1965)]. By means of the Cauchy companion augmentation operator, we obtain an equivalent form of Mehler’s formula. We also give several identities on the generating functions for products of the Al-Salam–Carlitz polynomials, which are extensions of the formulas for the Rogers–Szegö polynomials." @default.
• W3100331121 created "2020-11-23" @default.
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• W3100331121 date "2010-04-01" @default.
• W3100331121 modified "2023-09-25" @default.
• W3100331121 title "An operator approach to the Al-Salam–Carlitz polynomials" @default.
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• W3100331121 doi "https://doi.org/10.1063/1.3321603" @default.
• W3100331121 hasPublicationYear "2010" @default.
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