Integration of solutions of linear functional equations

DOI10.1080/10652469908819212zbMath0939.34059OpenAlexW2083121165MaRDI QIDQ4935269

Mark van Hoeij, Sergey A. Abramov

Publication date: 5 July 2000

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469908819212

zbMATH Keywords

integrationadjointsummationintegrating factorspecial functionOre ringhypergeometric sequence

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Linear functional-differential equations (34K06) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (14)

On the bottom summation ⋮ Telescoping in the context of symbolic summation in Maple ⋮ An algorithmic approach to the \(q\)-summability problem of bivariate rational functions ⋮ Hermite Reduction for D-finite Functions via Integral Bases ⋮ Stability Problems on D-finite Functions ⋮ Polynomial reduction for holonomic sequences and applications in \(\pi\)-series and congruences ⋮ Subanalytic solutions of linear difference equations and multidimensional hypergeometric sequences ⋮ Ore polynomial rings in one variable in computer algebra. ⋮ A new Sigma approach to multi-summation ⋮ Valuations of rational solutions of linear difference equations at irreducible polynomials ⋮ Detecting Nonexistence of Rational Solutions of Linear Difference Equations in Early Stages of Computation ⋮ Factorization of Polynomials and GCD Computations for Finding Universal Denominators ⋮ Integral Representation and Algorithms for Closed Form Summation ⋮ Differential Galois Theory and Integration

Cites Work

• \(q\)-hypergeometric solutions of \(q\)-difference equations
• Theory of non-commutative polynomials
• Decision procedure for indefinite hypergeometric summation
• Rational solutions of linear differential and difference equations with polynomial coefficients

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