关于q-求和与合流
On q-summation and confluence
摘要：
本文分为两个部分。在第一部分中，我们考虑了非正则奇异解析q-差分方程，其中q \in ] 0，1 [，并且我们证明了微分方程的发散解的Borel和如何在方便的扇区上被这样的q-差分方程的亚纯解一致逼近。在第二部分中，我们在假设q \in ]1，+ \infty [.在这种情况下，文献中广泛存在一个非正则奇异q-差分方程的发散解的至少四个不同的q-Borel和：在适当的假设下，我们阐明了它们之间的关系.
英文摘要：
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.
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