2024/09/09 by Dušan Popov, Popov, Dušan
Economics, Econometrics and Finance · Mathematics · #33C90 Applications of hypergeometric functions #33E20 Other functions defined by series and integrals #81R30 Coherent states #FOS: Physical sciences #Mathematical Approximation and Integration #Quantum Physics (quant-ph) #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2409.05476
openalex publication_date 2024/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present paper starts from a previously deduced result, in which the ν-function plays the role of the normalization function of generalized hypergeometric coherent states for quantum systems with a continuous spectrum. We have generalized this idea, obtaining a new function, the generalized ν-function. By defining a discrete-continuous limit, we revealed a series of interesting properties that, in the last instance, allow the formulation and solution of new integrals involving the generalized ν-functions which depend on both scalar arguments as well as those containing creation and annihilation operators, which generate the generalized hypergeometric coherent states. To our knowledge, the results obtained by us do not appear in the literature.