An Euler-type formula for \(\xi (2k+1)\)

DOI10.1016/j.jnt.2005.09.005zbMath1143.11028OpenAlexW2028078746MaRDI QIDQ852530

Michael J. Dancs, Tian-Xiao He

Publication date: 15 November 2006

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2005.09.005

zbMATH Keywords

Riemann zeta functionBernoulli numberEuler's formulaEuler polynomial

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Evaluation of number-theoretic constants (11Y60)

Related Items (11)

A Note on a Formula of Special Values of Dirichlet L-Functions ⋮ An Euler-type formula forβ(2n) and closed-form expressions for a class of zeta series ⋮ Certain relationships among polygamma functions, Riemann zeta function and generalized zeta function ⋮ A double inequality for the Apéry constant ⋮ Eulerian fractions and Stirling, Bernoulli and Euler functions with complex order parameters and their impact on the polylogarithm function ⋮ Eulerian polynomials and B-splines ⋮ On the fractional sums of some special functions ⋮ Asymptotic results of the remainders in the series representations for the Apéry constant ⋮ Numerical calculation of the Riemann zeta function at odd-integer arguments: a direct formula method ⋮ Numerical computation of the Riemann zeta function and prime counting function by using Gauss–Hermite and Gauss–Laguerre quadratures ⋮ A simpler proof of a Katsurada's theorem and rapidly converging series for \(\zeta (2n+1)\) and \(\beta (2n)\)

Cites Work

• An Elementary Proof of Euler's Formula for z(2m)

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