Infinite Summation Formulas Involving Riemann-Zeta function

zbMath1464.11087arXiv1908.09468MaRDI QIDQ5148714

Xueying Yuan, Xiaoxia Wang

Publication date: 5 February 2021

Full work available at URL: https://arxiv.org/abs/1908.09468

zbMATH Keywords

gamma functionRiemann zeta functionhypergeometric seriesgeneralized harmonic numbersinfinite summation formulas

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) (zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Generalized hypergeometric series, ({}_pF_q) (33C20)

Cites Work

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• The multiple zeta value data mine
• Dixon's \(_3F_2(1)\)-series and identities involving harmonic numbers and the Riemann zeta function
• On some series containing \(\psi{}(x)-\psi{}(y)\) and \((\psi{}(x)- \psi{}(y))^ 2\) for certain values of \(x\) and \(y\)
• Further summation formulae related to generalized harmonic numbers
• New series for some special values of $L$-functions
• Hypergeometric series and the Riemann zeta function
• A nonterminating 7F6-series evaluation
• Infinite summation formulas related to Riemann Zeta function from hypergeometric series
• On an Intriguing Integral and Some Series Related to ζ(4)
• Remarks on Some Integrals and Series Involving the Stirling Numbers and ζ(n)
• Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

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