Computing hypergeometric solutions of second order linear differential equations using quotients of formal solutions and integral bases

DOI10.1016/j.jsc.2016.11.014zbMath1375.65097arXiv1606.01576OpenAlexW2962841023MaRDI QIDQ2628322

Erdal Imamoglu, Mark van Hoeij

Publication date: 1 June 2017

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

Full work available at URL: https://arxiv.org/abs/1606.01576

zbMATH Keywords

algorithmsymbolic computationlinear differential equationsclosed form solutionshypergeometric solutionsintegral bases

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computation of special functions and constants, construction of tables (65D20) Linear ordinary differential equations and systems (34A30) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Classical hypergeometric functions, ({}_2F_1) (33C05)

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Uses Software

• ComputeBelyi
• hypergeometricsols

Cites Work

• Belyi functions for hyperbolic hypergeometric-to-Heun transformations
• Explicit formula for the generating series of diagonal 3D rook paths
• An algorithm for solving second order linear homogeneous differential equations
• An algorithm for computing an integral basis in an algebraic function field
• Computing Hypergeometric Solutions of Second Order Linear Differential Equations using Quotients of Formal Solutions
• Integral D-Finite Functions
• Second order differential equations with hypergeometric solutions of degree three
• Walks with small steps in the quarter plane
• Automatic Classification of Restricted Lattice Walks
• On Second Order Linear Differential Equations with Algebraic Solutions
• A polynomial reduction algorithm
• 2-descent for second order linear differential equations
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