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Resommation des series formelles

Resummation of formal series Solutions of second order linear complex ordinary differential equations near singularities

Solutions d'équations différentielles linéaires ordinaires du second ordre dans le champ complexe au voisinage de singularités irrégulières

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Summary

Formulae for solutions of complex ordinary differential equations in the neighbourhood of irregular singularities contain almost every time divergent series. The Resummation Theory developed in the field of Analytic Functional Equations by J.P. Ramis provides us with a tool-box to perform in different ways some effective calculations and to compare their results. We take full advantage of the possibilities of Computer Algebra, especially of exact rational evaluation.

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  1. Centre de Calcul du CNRS, BP 20 Cro, F-67037, Strasbourg-Cedex, France

    Jean Thomann

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  1. Jean Thomann
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Thomann, J. Resommation des series formelles. Numer. Math. 58, 503–535 (1990). https://doi.org/10.1007/BF01385638

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