# Accelero-summation of the formal solutions of nonlinear difference equations

@article{Immink2011AccelerosummationOT, title={Accelero-summation of the formal solutions of nonlinear difference equations}, author={Geertrui Klara Immink}, journal={Annales de l'Institut Fourier}, year={2011}, volume={61}, pages={1-51} }

In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of "level 1(+)". Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains; we prove that, under very general conditions, the formal solution is accelero-summable…

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