Ramanujan type \(1/\pi\) approximation formulas

DOI10.1016/j.jnt.2013.04.010zbMath1295.11142OpenAlexW1713779392MaRDI QIDQ740886

D. Kharzeev

Publication date: 9 September 2014

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2013.04.010

zbMATH Keywords

numerical methodselliptic functionsRamanujansingular modulus\(\pi\)-formulasalternative modular bases

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Theta series; Weil representation; theta correspondences (11F27) Evaluation of number-theoretic constants (11Y60)

Related Items (4)

On a Ramanujan-type series associated with the Heegner number 163 ⋮ Unnamed Item ⋮ Parametric evaluations of the Rogers-Ramanujan continued fraction ⋮ Conjectures on the evaluation of certain functions with algebraic properties

Cites Work

• Conjectures on the evaluation of alternative modular bases and formulas approximating \(1/\pi\)
• Class number three Ramanujan type series for \(1/\pi\)
• Evaluation of complete elliptic integrals of the first kind at singular moduli
• Ramanujan's series for \(1/\pi \) arising from his cubic and quartic theories of elliptic functions
• Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• Ramanujan and the Modular j-Invariant
• A Cubic Counterpart of Jacobi's Identity and the AGM
• Eisenstein series and approximations to \(\pi\)
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