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On the summability of the formal solutions of a class of inhomogeneous linear difference equations. (English) Zbl 0872.39002
The author discusses different equivalent ways of summing the formal solution $$\widehat{f}$$ of a linear difference equation $$y(z)-a(z)y(z+1)= b(z)$$, where $$a,b\in z^{-1}C\{z^{-1}\}$$ and $$\lim_{z\to\infty} za(z)\neq 0$$. The results obtained in this paper form an illustration of the theory of weak acceleration operators and cohensive functions of J. Ecalle [J. Anal. Math. 60, 71-97 (1993; Zbl 0808.30002)].