Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation (Q850522): Difference between revisions

Combinatorial identities that were needed in [\textit{J. A. C. Weidemann}, Quaest. Math. 28, No. 3, 375--390 (2005; Zbl 1085.41011)] are proved, mostly with C. Schneider's computer algebra package Sigma. The form of the Padé approximation of the logarithm of arbitrary order is stated as a conjecture.

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zbMATH Keywords

Padé approximation

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Combinatorial identities

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Computer algebra

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Creative telescoping

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reviewed by

Francisco Pérez Acosta

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describes a project that uses

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full work available at URL

https://doi.org/10.1007/s11139-006-6503-4

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cites work

Q4234305

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Q4726797

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On solutions of linear ordinary difference equations in their coefficient field

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Q5334359

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

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Decision procedure for indefinite hypergeometric summation

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Q4320535

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Solving difference equations in finite terms

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Q5529599

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Summation in Finite Terms

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Theory of summation in finite terms

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Q4341407

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Computer proofs of a new family of harmonic number identities.

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A \textit{Mathematica} version of Zeilberger's algorithm for proving binomial coefficient identities

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The solution of the problem of integration in finite terms

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Q4667612

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Degree bounds to find polynomial solutions of parameterized linear difference equations in \(\Pi\Sigma\)-fields

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Q3416425

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Solving parameterized linear difference equations in terms of indefinite nested sums and products

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Finding telescopers with minimal depth for indefinite nested sum and product expressions

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Padé Approximations to the Logarithm I: Derivation Via Differential Equations

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A fast algorithm for proving terminating hypergeometric identities

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Identifiers

zbMATH Open document ID

1102.41015

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Mathematics Subject Classification ID

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10.1007/S11139-006-6503-4

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Sitelinks

Mathematics(1 entry)

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+On solutions of linear ordinary difference equations in their coefficient field
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+Padé approximations to the logarithm. III: Alternative methods and additional results
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+Decision procedure for indefinite hypergeometric summation
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+Q4320535
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+Solving difference equations in finite terms
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+Computer proofs of a new family of harmonic number identities.
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+A \textit{Mathematica} version of Zeilberger's algorithm for proving binomial coefficient identities
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+The solution of the problem of integration in finite terms
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+Q4667612
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+Degree bounds to find polynomial solutions of parameterized linear difference equations in \(\Pi\Sigma\)-fields
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+Solving parameterized linear difference equations in terms of indefinite nested sums and products
+Normal rank
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+Finding telescopers with minimal depth for indefinite nested sum and product expressions
+Normal rank
@@ Property / cites work @@
+Padé Approximations to the Logarithm I: Derivation Via Differential Equations
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+A fast algorithm for proving terminating hypergeometric identities
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