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On a theorem of Maillet-Malgrange type for \(q\)-differential-difference equations. (Sur un théorème du type de Maillet-Malgrange pour les équations \(q\)-différences-différentielles.) (French) Zbl 0938.34064
Summary: The growth of the coefficients of a formal power series satisfying a holomorphic \(q\)-difference differential equation is described, where differential and \(q\)-difference operators are mixed. Following an idea of B. Malgrange [Asympt. Anal. 2, No. 1, 1-4 (1989; Zbl 0693.34004)] and using the implicit function theorem, a generalization of the Maillet-Malgrange theorem is established.

MSC:
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain
34K07 Theoretical approximation of solutions to functional-differential equations
Software:
ASYMPT
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