Series expansions for \(1/\pi^m\) and \(\pi^m\)

DOI10.1016/j.jmaa.2014.07.072zbMath1409.11143arXiv1311.6339OpenAlexW2020542497MaRDI QIDQ743193

Chuanan Wei, Xiaoxia Wang, Linlin Dai

Publication date: 23 September 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.6339

zbMATH Keywords

telescoping methodseries expansion for \(\pi^m\)series expansion for \(1/\pi^m\)

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Generalized hypergeometric series, ({}_pF_q) (33C20) Evaluation of number-theoretic constants (11Y60)

Related Items

$q$-analogues of several $\pi $-formulas

Cites Work

• A new Ramanujan-like series for \(1/\pi ^{2}\)
• \(\pi \)-formulas implied by Dougall's summation theorem for \(_{5} F _{4}\)-series
• \(\pi\)-formulas with free parameters
• A summation formula and Ramanujan type series
• Generators of some Ramanujan formulas
• Hypergeometric identities for 10 extended Ramanujan-type series
• Extensions of Ramanujan's two formulas for \(1/\pi\)
• Two hypergeometric summation theorems and Ramanujan-type series
• Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae
• Ramanujan's Series for 1/π: A Survey
• On the rapid computation of various polylogarithmic constants
• GAUSS SUMMATION AND RAMANUJAN-TYPE SERIES FOR 1/π
• Ramanujan-type formulae for $1/\pi$: A second wind?
• More Formulas for π
• A Simple Formula for &#960
• About a New Kind of Ramanujan-Type Series
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