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Problème de Riemann effectif et approximants de Padé-Hermite. (Effective Riemann problem and Padé-Hermite approximants). (French) Zbl 0768.11019
Approximations diophantiennes et nombres transcendants, C.-R. Colloq., Luminy/ Fr. 1990, 173-193 (1992).
The author gives a description of Fuchsian linear differential equations which are completely determined by their singular points, the local exponents and the existence of sufficiently many holomorphic solutions near the singularities. Hypergeometric functions in one variable form one class of examples, the Jordan-Pochhammer equation is another such class. The main point of the paper is that Chudnovsky’s monodromy trick to obtain explicit (gen explicit (generalised) Padé approximations for solutions and their derivatives can be applied to every such differential equation.
The first part of the paper classifies the ‘rigid’ Fuchsian equations, the second part applies Chudnovsky’s trick.
For the entire collection see [Zbl 0745.00060].

11J61 Approximation in non-Archimedean valuations
41A21 Padé approximation
34M99 Ordinary differential equations in the complex domain