English

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 n0(1)nn!xn+1\sum_{n\ge 0}(-1)^n\,n!\,x^{n+1}, 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 qq-difference operators associated with a given first order non-homogenous qq-difference equation, it will be shown that the summability order of qq-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}
}