The authors develop an R(p,q)-topological analysis framework including deformed Gamma functions, Banach and Frechet spaces, and analogues of Cauchy-Hadamard, Borel-Caratheodory, and Phragmen-Lindelof theorems for holomorphic functions.
Characterization of $({\cal R},p,q)-$deformed Rogers-Szeg\"o polynomials: associated quantum algebras, deformed Hermite polynomials and relevant properties
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abstract
This paper addresses a new characterization of $({\cal R},p,q)-$deformed Rogers-Szeg\"o polynomials by providing their three-term recurrence relation and the associated quantum algebra built with corresponding creation and annihilation operators. The whole construction is performed in a unified way, generalizing all known relevant results which are straightforwardly derived as particular cases. Continuous $({\cal R},p,q)-$deformed Hermite polynomials and their recurrence relation are also deduced. Novel relations are provided and discussed.
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math.QA 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Topological analysis in $\mathcal{R}(p,q)-$anisotropic sector and nuclear space on $\mathcal{R}(p,q)-$quantum deformed algebra
The authors develop an R(p,q)-topological analysis framework including deformed Gamma functions, Banach and Frechet spaces, and analogues of Cauchy-Hadamard, Borel-Caratheodory, and Phragmen-Lindelof theorems for holomorphic functions.