A new application of the Fox-Wright functions: the coherent states formalism
Abstract
In this paper we extend the applicability of Fox-Wright functions beyond mathematics, specifically in quantum physics. We focused our attention on a new application, on the connection between the Fox-Wright functions and the generalized coherent states formalism. We constructed the generalized coherent states in the Barut-Girardello manner, in which the Fox-Wright functions play the role of normalization functions, and we demonstrated that the Fox-Wright coherent states satisfy all general conditions imposed on the set of coherent states. In parallel, we examined the properties of both pure and mixed (thermal) Fox-Wright coherent states. All calculations were performed within the diagonal operators ordering technique (DOOT) using the Dirac's bra-ket formalism. Finally, we introduced some (specifically, integral) feedback elements that Fox-Wright coherent states induce in the theory of special functions, including a new integral representation of Fox-Wright functions.
Cite
@article{arxiv.2510.04874,
title = {A new application of the Fox-Wright functions: the coherent states formalism},
author = {Dusan Popov},
journal= {arXiv preprint arXiv:2510.04874},
year = {2025}
}
Comments
32 pages; No figures