Abstract
The “k-summable series” theory, recently developed by one of the authors (Ramis [6], [7]), and its applications to the theory of linear differential equations and linear difference equations prove that the evaluation of “actual-problems” related functions, known by its formal asymptotic expansions, is very often reduced (when k is rational) to the evaluation of a sum of a generalized factorial series. Usually for a given problem, one can choose among an infinite family of factorial series indexed by a continuous parameter ω ∈]ω0,+∞[(for 0 ≤ ω < ω0 the factorial series is divergent).
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© 1981 Springer-Verlag Berlin Heidelberg
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Ramis, J.P., Thomann, J. (1981). Some Comments About the Numerical Utilization of Factorial Series. In: Della Dora, J., Demongeot, J., Lacolle, B. (eds) Numerical Methods in the Study of Critical Phenomena. Springer Series in Synergetics, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81703-8_2
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DOI: https://doi.org/10.1007/978-3-642-81703-8_2
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