A Note on the Rogers-Szegö Polynomial q-Differential Operators

2024/11/04 by López, Ronald Orozco
#05A30 #33D15 #33D45 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.02680

Abstract

In this paper, we introduce the Rogers-Szegö deformed q-differential operators g_n(bD_q|u) based on q-differential operator D_q. The motivation for introducing the operators g_n(bD_q) is that their limit turns out to be the q-exponential operator T(bD_q) given by Chen. The deformed homogeneous Al-Salam-Carlitz polynomials Ψ_m^(q^-n)(ub,x|uq^-1) can easily be represented by using the operators g_n(bD_q|u). Identities relating the new general Al-Salam-Carlitz polynomial, defined by Cao et al., the generalized, and homogeneous Al-Salam-Carlitz polynomials Φ_m^(qn)(b,x|q) and basic hypergeometric series are given.

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