Further series representations for \(\zeta(2n+1)\)

DOI10.1016/S0096-3003(97)10145-XzbMath0939.11031OpenAlexW2041488234MaRDI QIDQ1127830

Hari M. Srivastava

Publication date: 3 September 1998

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(97)10145-x

zbMATH Keywords

functional equationRiemann zeta-functionBernoulli numbersHurwitz zeta functionsEuler's formulaharmonic numbersbinomial theoremPochhammer symbolEuler polynomialsl'Hôpital's rule

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) (zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Convergence and divergence of series and sequences of functions (40A30) Other functions defined by series and integrals (33E20) Hurwitz and Lerch zeta functions (11M35)

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Cites Work

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• Sums of certain series of the Riemann zeta function
• Some series representations of \(\zeta(2n+1)\)
• On evaluation of the Dirichlet series at positive integers by \(q\)- calculation
• On the zeta function values \(\zeta (2k+1)\), \(k=1, 2, \dots\)
• An Asymptotic Expansion for the First Derivative of the Generalized Riemann Zeta Function
• Some rapidly converging series for $\zeta (2n+1)$
• New rapidly convergent series representations for $\zeta (2n+1)$