Symbolic conversion of holonomic functions to hypergeometric type power series

DOI10.1134/S0361768822020104OpenAlexW4224282943MaRDI QIDQ2142982

Bertrand Teguia Tabuguia, Wolfram Koepf

Publication date: 30 May 2022

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

Full work available at URL: https://doi.org/10.1134/s0361768822020104

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Generalized hypergeometric series, ({}_pF_q) (33C20) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Uses Software

• gfun
• Maple
• Mathematica
• FPS
• DEtools

Cites Work

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• The concrete tetrahedron. Symbolic sums, recurrence equations, generating functions, asymptotic estimates
• The method of differentiating under the integral sign
• A holonomic systems approach to special functions identities
• Power series in computer algebra
• Hypergeometric solutions of linear recurrences with polynomial coefficients
• The algebra of holonomic equations
• Solving difference equations in finite terms
• Finite singularities and hypergeometric solutions of linear recurrence equations
• Representations of orthogonal polynomials
• Formal solutions to linear ordinary differential equations containing \(m\)-hypergeometric series
• \( m\)-fold hypergeometric solutions of linear recurrence equations revisited
• Special formal series solutions of linear operator equations
• \(m\)-sparse solution of linear ordinary differential equations with polynomial coefficients
• Computing hypergeometric solutions of linear recurrence equations
• GFUN

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