Harmonic number identities and Hermite-Padé approximations to the logarithm function

DOI10.1016/j.jat.2005.07.008zbMath1082.41014OpenAlexW2037364642MaRDI QIDQ2575616

Chu, Wenchang

Publication date: 5 December 2005

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2005.07.008

zbMATH Keywords

harmonic seriespartial fraction decompositiongeneralized Hermite-Padé approximantsnumber identities

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Padé approximation (41A21)

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Harmonic number identities via hypergeometric series and Bell polynomials ⋮ Some generalized q-harmonic number identities ⋮ Two problems of binomial sums involving harmonic numbers ⋮ A novel proof of two partial fraction decompositions ⋮ Riordan arrays and harmonic number identities ⋮ Summation formulas involving generalized harmonic numbers ⋮ Identities on harmonic and \(q\)-harmonic number sums ⋮ Several polynomials associated with the harmonic numbers ⋮ Generalized harmonic numbers with Riordan arrays ⋮ Series transformation formulas of Euler type, Hadamard product of series, and harmonic number identities ⋮ Harmonic number identities via the Newton-Andrews method ⋮ Unnamed Item ⋮ Watson-type₃F₂-series and summation formulae involving generalized harmonic numbers ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The Gauss₂F₁(1)-summation theorem and harmonic number identities ⋮ Dougall-Dixon formula and harmonic number identities ⋮ Dixon's \(_3F_2(1)\)-series and identities involving harmonic numbers and the Riemann zeta function ⋮ Partial-fraction decomposition of a rational function and its application ⋮ Summation formulae involving multiple harmonic numbers

Cites Work

• Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation
• Padé approximations to the logarithm. III: Alternative methods and additional results
• The special functions and their approximations. Vol. I, II
• Partial fractions and bilateral summations
• On the approximation of logarithms of algebraic numbers
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