A differential-equations approach to functional equivalence
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Generating functionology
Growth estimates for exp-log functions
Journal of Symbolic Computation
GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable
ACM Transactions on Mathematical Software (TOMS)
A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants
SIAM Journal on Matrix Analysis and Applications
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Asymptotic expansions of exp-log functions
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Algorithms for Formal Reduction of Vector Field Singularities
Journal of Dynamical and Control Systems
Journal of Symbolic Computation
Journal of Symbolic Computation
Guessing singular dependencies
Journal of Symbolic Computation
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Consider a power series f@?R[[z]], which is obtained by a precise mathematical construction. For instance, f might be the solution to some differential or functional initial value problem or the diagonal of the solution to a partial differential equation. In cases when no suitable method is available beforehand for determining the asymptotics of the coefficients f"n, but when many such coefficients can be computed with high accuracy, it would be useful if a plausible asymptotic expansion for f"n could be guessed automatically. In this paper, we will present a general scheme for the design of such ''asymptotic extrapolation algorithms''. Roughly speaking, using discrete differentiation and techniques from automatic asymptotics, we strip off the terms of the asymptotic expansion one by one. The knowledge of more terms of the asymptotic expansion will then allow us to approximate the coefficients in the expansion with high accuracy.