An algorithm for computing a standard form for second-order linear \(q\)-difference equations

DOI10.1016/S0022-4049(97)00017-0zbMath0877.12004MaRDI QIDQ1358917

Peter A. Hendriks

Publication date: 26 November 1997

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

algorithmGalois theorysystems of linear difference equationsstandard form for second-order linear \(q\)-difference equations

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Explicit solutions, first integrals of ordinary differential equations (34A05) Difference algebra (12H10)

Related Items (11)

Differential transcendence of solutions for 𝑞-difference equation of Ramanujan function ⋮ Computing differential Galois groups of second-order linear \(q\)-difference equations ⋮ Fast computation of the \(N\)-th term of a \(q\)-holonomic sequence and applications ⋮ On the algebraic relations between Mahler functions ⋮ On the computation of the Galois group of linear difference equations ⋮ Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation ⋮ Differential Galois theory of linear difference equations ⋮ Galois groups for integrable and projectively integrable linear difference equations ⋮ Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions ⋮ Difference Algebra ⋮ Hypertranscendence and linear difference equations

Cites Work

• An algorithm for solving second order linear homogeneous differential equations
• An algorithm determining the difference Galois group of second order linear difference equations
• Galois Cohomology
• Galois theory of difference equations
• Galois action on solutions of a differential equation

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