Indefinite summation with unspecified summands

DOI10.1016/j.disc.2006.04.005zbMath1157.05006OpenAlexW2102658840MaRDI QIDQ2501544

Carsten Schneider, Manuel Kauers

Publication date: 14 September 2006

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2006.04.005

zbMATH Keywords

combinatorial identitiesdifference fieldssymbolic summation

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Difference algebra (12H10)

Related Items (13)

Combinatorial identities involving reciprocals of the binomial and central binomial coefficients and harmonic numbers ⋮ Refined telescoping algorithms in RΠΣ -extensions to reduce the degrees of the denominators✱ ⋮ Representation of hypergeometric products of higher nesting depths in difference rings ⋮ A symbolic summation approach to Feynman integral calculus ⋮ Summation theory. II: Characterizations of \(R {\Pi}{\Sigma}^{\ast}\)-extensions and algorithmic aspects ⋮ A refined difference field theory for symbolic summation ⋮ A difference ring theory for symbolic summation ⋮ Rational solutions of ordinary difference equations ⋮ Structural theorems for symbolic summation ⋮ SIMPLIFYING SUMS IN ΠΣ*-EXTENSIONS ⋮ On rational and hypergeometric solutions of linear ordinary difference equations in \(\Pi\Sigma^\ast\)-field extensions ⋮ Rational solutions of first-order algebraic ordinary difference equations ⋮ Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation

Uses Software

• qZeil
• SIGMA

Cites Work

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• Decision procedure for indefinite hypergeometric summation
• Computer proofs for polynomial identities in arbitrary many variables
• Symbolic summation with single-nested sum extensions
• Finding telescopers with minimal depth for indefinite nested sum and product expressions
• Solving parameterized linear difference equations in terms of indefinite nested sums and products
• The Problem of Integration in Finite Terms
• The solution of the problem of integration in finite terms

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