Algorithmic determination of \(q\)-power series for \(q\)-holonomic functions

DOI10.1016/j.jsc.2011.12.004zbMath1245.33016OpenAlexW2573304MaRDI QIDQ412219

Wolfram Koepf, Torsten Sprenger

Publication date: 4 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2011.12.004

zbMATH Keywords

orthogonal polynomials\(q\)-hypergeometric functionsMaple\(q\)-holonomic functionsFPS algorithm

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (4)

Fast computation of the \(N\)-th term of a \(q\)-holonomic sequence and applications ⋮ On solutions of holonomic divided-difference equations on nonuniform lattices ⋮ \( m\)-fold hypergeometric solutions of linear recurrence equations revisited ⋮ Representations of \(q\)-orthogonal polynomials

Uses Software

• Maple
• qGeneratingFunctions

Cites Work

• Unnamed Item
• Unnamed Item
• A Mathematica package for \(q\)-holonomic sequences and power series
• A holonomic systems approach to special functions identities
• Power series in computer algebra
• Finite singularities and hypergeometric solutions of linear recurrence equations
• On Zeilberger's algorithm and its \(q\)-analogue
• \(q\)-hypergeometric solutions of \(q\)-difference equations
• Special formal series solutions of linear operator equations
• Algorithms for \(q\)-hypergeometric summation in computer algebra
• Computing hypergeometric solutions of linear recurrence equations
• Properties ofq-holonomic functions
• On a structure formula for classical \(q\)-orthogonal polynomials
• Quantum calculus

This page was built for publication: Algorithmic determination of \(q\)-power series for \(q\)-holonomic functions