A Mathematica package for \(q\)-holonomic sequences and power series

DOI10.1007/s11139-008-9132-2zbMath1180.33030OpenAlexW2072344980MaRDI QIDQ1037558

Christoph Koutschan, Manuel Kauers

Publication date: 16 November 2009

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-008-9132-2

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Additive difference equations (39A10) Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.) (68N30) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items

Linked partition ideals and the Alladi-Schur theorem ⋮ Polynomial identities implying Capparelli's partition theorems ⋮ Linked partition ideals and kanade-Russell conjectures ⋮ Fast computation of the \(N\)-th term of a \(q\)-holonomic sequence and applications ⋮ Sequences in overpartitions ⋮ Algorithmic determination of \(q\)-power series for \(q\)-holonomic functions ⋮ Linked partition ideals, directed graphs and \(q\)-multi-summations ⋮ Reproducing kernel bounds for an advanced wavelet frame via the theta function ⋮ New infinite hierarchies of polynomial identities related to the Capparelli partition theorems ⋮ Extended rate, more GFUN ⋮ The \(\mathfrak {sl}_{3}\) Jones polynomial of the trefoil: a case study of \(q\)-holonomic sequences ⋮ \texttt{qFunctions} -- a Mathematica package for \(q\)-series and partition theory applications ⋮ qGeneratingFunctions ⋮ An extension of holonomic sequences: \(C^2\)-finite sequences

Uses Software

• gfun
• Maple
• Mathematica
• qMultiSum
• qZeil
• RATE
• Guess
• Telescopers
• GeneratingFunctions

Cites Work

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• Non-commutative elimination in Ore algebras proves multivariate identities
• On Zeilberger's algorithm and its \(q\)-analogue
• Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type
• \texttt{qMultiSum} -- a package for proving \(q\)-hypergeometric multiple summation identities
• An infinite family of Engel expansions of Rogers-Ramanujan type
• On a conjecture of Peter Borwein
• A \textit{Mathematica} version of Zeilberger's algorithm for proving binomial coefficient identities
• Telescoping in the context of symbolic summation in Maple
• Some identities for terminating q-series
• GFUN
• Properties ofq-holonomic functions
• On identities of the Rogers-Ramanujan type