Novel theorem develops generating functions for modeling quantum oscillators, indicating methods for complex interactions.
In this study, through the utilization of properties associated with symmetric functions, we establish a novel theorem and develop generating functions of the products of Gaussian numbers with numbers, bivariate polynomials and certain polynomials. As an application, we use these generating functions for modeling the quantum oscillators with complex interactions.
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Hamek et al. (2026) studied this question.
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