A differential-equations approach to functional equivalence
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Fast evaluation of holonomic functions
Theoretical Computer Science - Special issue on real numbers and computers
Fast evaluation of holonomic functions near and in regular singularities
Journal of Symbolic Computation
Journal of Symbolic Computation
A new zero-test for formal power series
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Good reduction of Puiseux series and applications
Journal of Symbolic Computation
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One approach for computations with special functions in computer algebra is the systematic use of analytic functions whenever possible. This naturally leads to problems of how to answer questions about analytic functions in a fully effective way. Such questions comprise the determination of the radius of convergence or the evaluation of the analytic continuation of the function at the endpoint of a broken line path. In this paper, we propose a first definition for the notion of an effective analytic function and we show how to effectively solve several types of differential equations in this context. We will limit ourselves to functions in one variable.