Liouvillian solutions of linear differential equations of order three and higher

DOI10.1006/jsco.1999.0316zbMath0997.12011OpenAlexW1966728617MaRDI QIDQ1974703

Felix Ulmer, Jean-François Ragot, Mark van Hoeij, Jacques-Arthur Weil

Publication date: 8 May 2000

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.1999.0316

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Linear ordinary differential equations and systems (34A30) Abstract differential equations (12H20)

Related Items (18)

Absolute reducibility of differential operators and Galois groups ⋮ Solutions of algebraic linear ordinary differential equations ⋮ Lifting and recombination techniques for absolute factorization ⋮ A characterization of reduced forms of linear differential systems ⋮ An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations ⋮ Schwarz maps of algebraic linear ordinary differential equations ⋮ On the Liouvillian solutions to the perturbation equations of the Schwarzschild black hole ⋮ Reduced forms of linear differential systems and the intrinsic Galois-Lie algebra of Katz ⋮ Rational solutions of first order algebraic ordinary differential equations ⋮ Liouvillian solutions of third order differential equations ⋮ A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs ⋮ Extensions of differential representations of SL₂ and tori ⋮ Zariski closures of reductive linear differential algebraic groups ⋮ Effective descent for differential operators ⋮ Differential equations and finite groups ⋮ Classes of elementary function solutions to the CEV model I ⋮ Effective Set Membership in Computer Algebra and Beyond ⋮ Note on algebraic solutions of differential equations with known finite Galois group

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