2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155738This 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.36 pages. Following the referee's comments, we have clarified the exposition of some proofs and corrected some misprintsClassical Analysis and ODEsQuantum Algebra34M30, 39A13, 33D05text