In this paper, we study power series in several variables, which are completely determined as solutions of sets of differential equations with initial conditions. We introduce a large class of such power series, which we call “D-algebraic”. We prove several closure properties for this class and give an effective zero test for D-algebraic series.

Keywords: D-algebraic series, algorithm, zero-test

A.M.S. subject classification: 69W30, 11Y60, 34-04, 35-04, 12H05, 40-04, 13P10

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