On q-summation and confluence
Classical Analysis and ODEs
2008-02-28 v2 Quantum Algebra
Abstract
This paper is divided in two parts. In the first part we consider irregular singular analytic q-difference equations, with q\in ]0,1[, and we show how the Borel sum of a divergent solution of a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of such a q-difference equation. In the second part, we work under the assumption q\in ]1,+\infty[. In this case, at least four different q-Borel sums of a divergent solution of an irregular singular analytic q-difference equations are spread in the literature: under convenient assumptions we clarify the relations among them.
Cite
@article{arxiv.0709.1610,
title = {On q-summation and confluence},
author = {Lucia Di Vizio and Changgui Zhang},
journal= {arXiv preprint arXiv:0709.1610},
year = {2008}
}
Comments
36 pages. Following the referee's comments, we have clarified the exposition of some proofs and corrected some misprints