On the positive powers of $q$-analogs of Euler series
Number Theory
2021-07-09 v1
Abstract
The most simple and famous divergent power series coming from ODE may be the so-called Euler series , that, as well as all its positive powers, is Borel-summable in any direction excepted the negative real half-axis. By considering a family of linear -difference operators associated with a given first order non-homogenous -difference equation, it will be shown that the summability order of -analoguous counterparties of Euler series depends upon of the degree of power under consideration.
Keywords
Cite
@article{arxiv.2107.03536,
title = {On the positive powers of $q$-analogs of Euler series},
author = {Changgui Zhang},
journal= {arXiv preprint arXiv:2107.03536},
year = {2021}
}