The Gauss2F1(1)-summation theorem and harmonic number identities

DOI10.1080/10652460903016166zbMath1179.33005OpenAlexW2069925384MaRDI QIDQ3651174

Chu, Wenchang, Xiaojing Chen

Publication date: 8 December 2009

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460903016166

zbMATH Keywords

Riemann zeta seriesBell polynomialsHypergeometric seriesgeneralized harmonic numbersGauss' summation formula

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (11)

Harmonic number identities via hypergeometric series and Bell polynomials ⋮ Infinite series identities on harmonic numbers ⋮ Euler sums and Stirling sums ⋮ Explicit formulas of Euler sums via multiple zeta values ⋮ Summation formulas involving generalized harmonic numbers ⋮ Gauss's theorem and harmonic number summation formulae with certain mathematical constants ⋮ Harmonic-number summation identities, symmetric functions, and multiple zeta values ⋮ Series transformation formulas of Euler type, Hadamard product of series, and harmonic number identities ⋮ Harmonic number identities via the Newton-Andrews method ⋮ Watson-type₃F₂-series and summation formulae involving generalized harmonic numbers ⋮ Unnamed Item

Uses Software

• SIGMA

Cites Work

• Unnamed Item
• Hypergeometric approach to Weideman's conjecture
• On some series containing \(\psi{}(x)-\psi{}(y)\) and \((\psi{}(x)- \psi{}(y))^ 2\) for certain values of \(x\) and \(y\)
• Certain classes of infinite series
• On some log-cosine integrals related to \(\zeta(3), \zeta(4)\), and \(\zeta(6)\).
• Computer proofs of a new family of harmonic number identities.
• Hypergeometric series and harmonic number identities
• Harmonic number identities and Hermite-Padé approximations to the logarithm function
• Further summation formulae related to generalized harmonic numbers

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