Rational solutions of linear difference and \(q\)-differential equations with polynomial coefficients

zbMath0910.65107MaRDI QIDQ1276507

Sergey A. Abramov

Publication date: 31 January 1999

Published in: Programming and Computer Software (Search for Journal in Brave)

zbMATH Keywords

algorithm\(q\)-difference equationspolynomial coefficientslinear difference equationrational solutionhypergeometric right-hand

Mathematics Subject Classification ID

Related Items (20)

Computing solutions of linear Mahler equations ⋮ An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations ⋮ \(q\)-hypergeometric solutions of \(q\)-difference equations ⋮ Fast computation of the \(N\)-th term of a \(q\)-holonomic sequence and applications ⋮ The factorial-basis method for finding definite-sum solutions of linear recurrences with polynomial coefficients ⋮ Computing hypergeometric solutions of linear recurrence equations ⋮ Apparent singularities of linear difference equations with polynomial coefficients ⋮ \( m\)-fold hypergeometric solutions of linear recurrence equations revisited ⋮ Particular solutions of linear differential and (\(q\)-) difference systems with hypergeometric right-hand sides ⋮ Indicial rational functions of linear ordinary differential equations with polynomial coefficients ⋮ Algorithms for \(q\)-hypergeometric summation in computer algebra ⋮ Perfect bases for differential equations ⋮ Multibasic and mixed hypergeometric Gosper-type algorithms ⋮ Polynomial solutions of a nonlinear difference equation ⋮ Denominators of rational solutions of linear difference systems of an arbitrary order ⋮ Detecting Nonexistence of Rational Solutions of Linear Difference Equations in Early Stages of Computation ⋮ Factorization of Polynomials and GCD Computations for Finding Universal Denominators ⋮ Linear differential and difference systems: \(\mathrm{EG}_\delta\)- and \(\mathrm{EG}_\sigma\)-eliminations ⋮ Length enumeration of fully commutative elements in finite and affine Coxeter groups ⋮ On solutions of linear ordinary difference equations in their coefficient field

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