Kovacic's algorithm and its application to some families of special functions

DOI10.1007/BF01268661zbMath0785.12003OpenAlexW2086501442MaRDI QIDQ1205132

Anne Duval, Michèle Loday-Richaud

Publication date: 1 April 1993

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01268661

zbMATH Keywords

Riccati equationdifferential Galois groupclosed form solutionsecond order linear differential equationLiouvillian solutionsHeun's equationhypergeometric equationconfluent equation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Explicit solutions, first integrals of ordinary differential equations (34A05) Differential algebra (12H05)

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Cites Work

• A solution spectrum of the nonlinear Schrödinger equation. II
• MACSYMA from F to G
• An algorithm for solving second order linear homogeneous differential equations
• On Liouvillian solutions of linear differential equations
• [https://portal.mardi4nfdi.de/wiki/Publication:3029104 Liouvillian Solutions of the Differential Equation y � � + S(x)y = 0 with S(x) Binomial]
• Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations
• Galois groups and elementary solutions of some linear differential equations.
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