Padé approximations to the logarithm. III: Alternative methods and additional results

DOI10.1007/s11139-006-0144-5zbMath1108.41011OpenAlexW2063265860MaRDI QIDQ874896

J. A. C. Weideman, Carsten Schneider, Kathy A. Driver, Prodinger, Helmut

Publication date: 10 April 2007

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

Full work available at URL: https://doi.org/10.1007/s11139-006-0144-5

zbMATH Keywords

Padé approximationComputer algebraCombinatorial identitiesCreative telescoping

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Padé approximation (41A21) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items

Harmonic number identities via hypergeometric series and Bell polynomials, Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation, Riordan arrays and harmonic number identities, On congruences related to central binomial coefficients, A refined difference field theory for symbolic summation, Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms, Harmonic number identities via the Newton-Andrews method, SIMPLIFYING SUMS IN ΠΣ*-EXTENSIONS, Dougall-Dixon formula and harmonic number identities, Simplifying Multiple Sums in Difference Fields, Dixon's \(_3F_2(1)\)-series and identities involving harmonic numbers and the Riemann zeta function, Harmonic number identities and Hermite-Padé approximations to the logarithm function, Degree bounds to find polynomial solutions of parameterized linear difference equations in \(\Pi\Sigma\)-fields

Uses Software

• SIGMA

Cites Work

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• Degree bounds to find polynomial solutions of parameterized linear difference equations in \(\Pi\Sigma\)-fields
• Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation
• A fast algorithm for proving terminating hypergeometric identities
• Theory of summation in finite terms
• The umbral calculus
• Solving difference equations in finite terms
• Computer proofs of a new family of harmonic number identities.
• On solutions of linear ordinary difference equations in their coefficient field
• A \textit{Mathematica} version of Zeilberger's algorithm for proving binomial coefficient identities
• Summation in Finite Terms
• Applications of Basic Hypergeometric Functions
• Decision procedure for indefinite hypergeometric summation
• 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
• Padé Approximations to the Logarithm I: Derivation Via Differential Equations