A computable extension for D-finite functions: DD-finite functions

DOI10.1016/j.jsc.2018.07.002zbMath1427.13034OpenAlexW2885969493MaRDI QIDQ2422706

Antonio Jiménez-Pastor, Veronika Pillwein

Publication date: 20 June 2019

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2018.07.002

zbMATH Keywords

holonomic functionsclosure propertiesformal power series

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Derivations and commutative rings (13N15) Formal power series rings (13F25)

Related Items (6)

Autonomous first order differential equations ⋮ The six-vertex model on random planar maps revisited ⋮ On the exponential generating function of labelled trees ⋮ DD-finite functions in Sage ⋮ An extension of holonomic sequences: \(C^2\)-finite sequences ⋮ DD-Finite Functions Implemented in Sage

Uses Software

• gfun
• SageMath
• DLMF
• GeneratingFunctions
• ore_algebra

Cites Work

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• On full rank differential systems with power series coefficients
• The concrete tetrahedron. Symbolic sums, recurrence equations, generating functions, asymptotic estimates
• Differentiably finite power series
• Formal solutions and factorization of differential operators with power series coefficients
• Regular solutions of linear differential systems with power series coefficients
• On the non-holonomic character of logarithms, powers, and the \(n\)th prime function
• Ore Polynomials in Sage
• Matrix Analysis
• GFUN
• Algorithmic Arithmetics with DD-Finite Functions
• The Holonomic Toolkit

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