Taiwanese Journal of Mathematics

Notes On Carlitz's q-Operators

Jian Cao

Full-text: Open access

Abstract

In this paper, Carlitz’s $q$-operator and the auxiliary ones are applied to prove $q$-Christoffel-Darboux formulas and some Carlitz type generating functions. In addition, the technique of exponential operator decomposition to deduce $q$-Mehler’s formulas for Rogers-Szego and Hahn polynomials are shown.

Article information

Source
Taiwanese J. Math., Volume 14, Number 6 (2010), 2229-2244.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406072

Digital Object Identifier
doi:10.11650/twjm/1500406072

Mathematical Reviews number (MathSciNet)
MR2742361

Zentralblatt MATH identifier
1219.05008

Subjects
Primary: 05A30: $q$-calculus and related topics [See also 33Dxx] 11B65: Binomial coefficients; factorials; $q$-identities [See also 05A10, 05A30] 33D15: Basic hypergeometric functions in one variable, $_r\phi_s$ 33D45: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)

Keywords
Carlitz's $q$-operators Rogers-Szegö polynomials $q$-Mehler's formula Hahn polynomials $q$-Christoffel-Darboux formulas exponential operator decomposition

Citation

Cao, Jian. Notes On Carlitz's q-Operators. Taiwanese J. Math. 14 (2010), no. 6, 2229--2244. doi:10.11650/twjm/1500406072. https://projecteuclid.org/euclid.twjm/1500406072


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