Résumé : In this talk, we consider linear differential systems of first order (equivalently linear differential equations of arbitrary order), and we question whether they can be solved in terms of generalized hypergeometric functions. This question is motivated by the many properties of the latter which arise in physics and combinatorics. It has been tackled in the literature for second-order differential equations, namely Bessel's, Whittaker's, Kummer's, and Gauss's. We propose a new algorithm which surpasses the restrictions on the dimension of the system, and equivalently on the order of the equation. This is joint work with Frédéric Chyzak.

Dernière modification : Monday 27 May 2024

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