RAMANUJAN SERIES UPSIDE-DOWN

DOI10.1017/S1446788714000147zbMath1305.33014arXiv1206.3981OpenAlexW2041457691MaRDI QIDQ2877690

Jesús Guillera, Mathew D. Rogers

Publication date: 25 August 2014

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.3981

zbMATH Keywords

hypergeometric seriesDirichlet \(L\)-valuesRamanujan type formulas for \(1/\pi\)

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Holomorphic modular forms of integral weight (11F11) Generalized hypergeometric series, ({}_pF_q) (33C20) Elliptic functions and integrals (33E05) Evaluation of number-theoretic constants (11Y60) Elliptic integrals as hypergeometric functions (33C75)

Related Items (5)

Solvable lattice sums and quadratic Dirichlet $L$-values ⋮ A hypergeometric version of the modularity of rigid Calabi-Yau manifolds ⋮ New series for powers of \(\pi\) and related congruences ⋮ RAMANUJAN SERIES WITH A SHIFT ⋮ Common extension of the Watson and Whipple sums and Ramanujan-likeπ-formulae

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Hypergeometric identities for 10 extended Ramanujan-type series
• Apéry limits and special values of \(L\)-functions
• Ramanujan's series for \(1/\pi \) arising from his cubic and quartic theories of elliptic functions
• WZ-Proofs of “Divergent” Ramanujan-Type Series
• Rational analogues of Ramanujan's series for 1/π
• Dirichlet L -series with real and complex characters and their application to solving double sums
• Some entries in Ramanujan's notebooks

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