SIMPLIFYING SUMS IN ΠΣ*-EXTENSIONS
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Publication:3595327
DOI10.1142/S0219498807002302zbMath1120.33023OpenAlexW1995044098MaRDI QIDQ3595327
Publication date: 10 August 2007
Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0219498807002302
Symbolic computation and algebraic computation (68W30) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10) Difference algebra (12H10)
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Cites Work
- Unnamed Item
- Rational normal forms and minimal decompositions of hypergeometric terms
- Degree bounds to find polynomial solutions of parameterized linear difference equations in \(\Pi\Sigma\)-fields
- Padé approximations to the logarithm. III: Alternative methods and additional results
- Solving difference equations in finite terms
- A kind of binomial identity
- On Zeilberger's algorithm and its \(q\)-analogue
- Computer proofs of a new family of harmonic number identities.
- On solutions of linear ordinary difference equations in their coefficient field
- Product representations in \(\Pi\Sigma\)-fields
- Polynomial algorithms in computer algebra
- Greatest factorial factorization and symbolic summation
- A \textit{Mathematica} version of Zeilberger's algorithm for proving binomial coefficient identities
- Multibasic and mixed hypergeometric Gosper-type algorithms
- Indefinite summation with unspecified summands
- Summation in Finite Terms
- Decision procedure for indefinite hypergeometric summation
- Solving parameterized linear difference equations in terms of indefinite nested sums and products
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