Generalizing the Index of the Deformed Rogers-Szegö Polynomials and the q-Exponential Operator

2024/08/16 by López, Ronald Orozco
#33D15 #33D45 #Combinatorics (math.CO) #FOS: Mathematics #Primary 05A30. Secondary 11B39

paper · doi:10.48550/arxiv.2408.08943

Abstract

This paper introduces the deformed Rogers-Szegö functions \rm R_α(x,y;u,v|q). When α=-n is a negative integer, these functions are related to the q-derivatives of Ramanujan's partial Theta function. Basic properties of the polynomial \rm R_α are given, along with recurrence relations, its representations, and generating functions. We use the u-deformed q-exponential operator \rm T(qD_q|u) to obtain identities for Rogers-Szegö functions, in particular, Rogers-type formulas.

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