Can Umbral and $q$-calculus be merged?
Classical Analysis and ODEs
2019-09-04 v1
Abstract
The -calculus is reformulated in terms of the umbral calculus and of the associated operational formalism. We show that new and interesting elements emerge from such a restyling. The proposed technique is applied to a different formulations of special functions, to the derivation of integrals involving ordinary and -functions and to the study of -special functions and polynomials.
Cite
@article{arxiv.1909.00058,
title = {Can Umbral and $q$-calculus be merged?},
author = {G. Dattoli and B. Germano and K. Górska and M. R. Martinelli},
journal= {arXiv preprint arXiv:1909.00058},
year = {2019}
}