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On q-summation and confluence

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.
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Submitted on : Wednesday, January 7, 2009 - 3:17:13 PM
Last modification on : Tuesday, December 8, 2020 - 11:00:00 AM

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Lucia Di Vizio, Changgui Zhang. On q-summation and confluence. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2009, 59 (1), pp.347-392. ⟨10.5802/aif.2433⟩. ⟨hal-00350701⟩

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