Analysis reveals new identities and properties of Rogers-Szego polynomials, suggesting advancements in algebraic structures.
This paper addresses the generalized Cauchy operator and its properties. Moreover, the construction of the homogeneous Rogers-Szegö polynomials and identities such as the generating function, Mehler and Rogers formulas as well as extended identities for the generalized homogeneous Rogers-Szegö polynomials are provided in the framework of the [Formula: see text]-deformed algebras.
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Hounkonnou et al. (2025) studied this question.
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