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On q -summation and confluence

Lucia Di VizioChanggui Zhang — 2009

Annales de l’institut Fourier

This paper is divided in two parts. In the first part we study a convergent q -analog of the divergent Euler series, with q ( 0 , 1 ) , and we show how the Borel sum of a generic Gevrey formal solution to a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of a corresponding q -difference equation. In the second part, we work under the assumption q ( 1 , + ) . In this case, at least four different q -Borel sums of a divergent power series solution of an irregular singular...

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