Borwein and Bradley's Apérv-Like Formulae for ζ(4n + 3)

DOI10.1080/10586458.1999.10504398zbMath0976.11035OpenAlexW2012715911MaRDI QIDQ4523662

Gert Almkvist, Andrew Granville

Publication date: 14 January 2001

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/233755

zbMATH Keywords

Riemann zeta-functionidentityBorwein-Bradley formula

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06)

Related Items (15)

“Divergent” Ramanujan-type supercongruences ⋮ Infinite series identities derived from the very well-poised \(\Omega\)-sum ⋮ THIRTY-TWO GOLDBACH VARIATIONS ⋮ INFINITE SERIES WITH HARMONIC NUMBERS AND CENTRAL BINOMIAL COEFFICIENTS ⋮ A \(q\)-analogue of the Bailey-Borwein-Bradley identity ⋮ \(p\)-adic congruences motivated by series ⋮ Integral representation of sums of series associated with special functions ⋮ Alternating multiple zeta values, and explicit formulas of some Euler-Apéry-type series ⋮ On one method for fast approximation of zeta constants by rational fractions ⋮ More congruences for central binomial coefficients ⋮ Selected Applications of LLL in Number Theory ⋮ Further Apéry-like series for Riemann zeta function ⋮ A bivariate generating function for zeta values and related supercongruences ⋮ Alternating series of Apéry-type for the Riemann zeta function. ⋮ Computational strategies for the Riemann zeta function

Cites Work

• Letter
• On the series \(\sum ^{\infty}_{k=1}\binom{2k}{k}^{-1}k^{-n}\) and related sums
• Some new identities for \(\zeta(k)\).
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• Interesting Series Involving the Central Binomial Coefficient
• Empirically Determined Apéry-Like Formulae for ζ(4n+3)

This page was built for publication: Borwein and Bradley's Apérv-Like Formulae for ζ(4n + 3)