42 citations · 260 across the 31 of their papers we have counts for
8 papers · 1 filter
Representability of G-functions as rational functions in hypergeometric series
Thomas Dreyfus, Tanguy Rivoal
Fresán and Jossen have given a negative answer to a question of Siegel about the representability of every -function as a polynomial with algebraic coefficients in -functions…
Differential Galois Theory and Integration
Thomas Dreyfus, Jacques-Arthur Weil
In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illus…
Degeneration from difference to differential Okamoto spaces for the sixth Painlevé equation
Thomas Dreyfus, Viktoria Heu
In the current paper we study the -analogue introduced by Jimbo and Sakai of the well known Painlevé VI differential equation. We explain how it can be deduced from a -analog…
On the multiple-scale analysis for some linear partial -difference and differential equations with holomorphic coefficients
Thomas Dreyfus, Alberto Lastra, Stéphane Malek
The analytic and formal solutions of certain family of -difference-differential equations under the action of a complex perturbation parameter is considered. The previous study…
Liouville integrability: an effective Morales-Ramis-Simó theorem
Ainhoa Aparicio-Monforte, Thomas Dreyfus, Jacques-Arthur Weil
Consider a complex Hamiltonian system and an integral curve. In this paper, we give an effective and efficient procedure to put the variational equation of any order along the inte…
Confluence of meromorphic solutions of q-difference equations
Thomas Dreyfus
In this paper, we consider a q-analogue of the Borel-Laplace summation where q>1 is a real parameter. In particular, we show that the Borel-Laplace summation of a divergent power s…
A density theorem for parameterized differential Galois theory
Thomas Dreyfus
We study parameterized linear differential equations with coefficients depending meromorphically upon the parameters. As a main result, analogously to the unparameterized density t…
Computing the Galois group of some parameterized linear differential equation of order two
Thomas Dreyfus
We extend Kovacic's algorithm to compute the differential Galois group of some second order parameterized linear differential equation. In the case where no Liouvillian solutions c…