Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae

DOI10.1090/S0025-5718-2011-02474-9zbMath1233.33002OpenAlexW2093914771MaRDI QIDQ3094289

Chu, Wenchang

Publication date: 24 October 2011

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2011-02474-9

zbMATH Keywords

Abel's lemma on summation by partsclassical hypergeometric seriesDougall's bilateral \(_{2}H_{2}\)-series identityRamanujan's \(\pi\)-formulaethe Gauss summation theorem

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Approximation to limiting values (summation of series, etc.) (40A25) Numerical summation of series (65B10) Evaluation of number-theoretic constants (11Y60)

Related Items (28)

Infinite series identities derived from the very well-poised \(\Omega\)-sum ⋮ Hidden \(q\)-analogues of Ramanujan-like \(\pi\)-series ⋮ From Wallis and Forsyth to Ramanujan ⋮ More hypergeometric identities related to Ramanujan-type series ⋮ GAUSS SUMMATION AND RAMANUJAN-TYPE SERIES FOR 1/π ⋮ A series evaluation technique based on a modified Abel lemma ⋮ INFINITE SERIES CONCERNING HARMONIC NUMBERS AND QUINTIC CENTRAL BINOMIAL COEFFICIENTS ⋮ Infinite series about harmonic numbers inspired by Ramanujan-like formulae ⋮ Infinite series of convergence rate $-1/8$ suggested by two formulae of Guillera ⋮ Extensions of Ramanujan's two formulas for \(1/\pi\) ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Evaluation of Apéry-like series through multisection method ⋮ Hypergeometric series summations and \(\pi\)-formulas ⋮ \(\pi\)-formulas with free parameters ⋮ Harmonic sums from the Kummer theorem ⋮ Further Apéry-like series for Riemann zeta function ⋮ $q$-analogues of several $\pi $-formulas ⋮ Series expansions for \(1/\pi^m\) and \(\pi^m\) ⋮ Ramanujan-like formulae for \(\pi\) and \(1/\pi\) via Gould-Hsu inverse series relations ⋮ Extensions of the classical theorems for very well-poised hypergeometric functions ⋮ A summation formula and Ramanujan type series ⋮ Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients ⋮ q-Analogues of Guillera’s two series for π±2 with convergence rate 27 64 ⋮ Common extension of the Watson and Whipple sums and Ramanujan-likeπ-formulae ⋮ Two hypergeometric summation theorems and Ramanujan-type series ⋮ Series with harmonic-like numbers and squared binomial coefficients ⋮ NEW SERIES IDENTITIES FOR ${\frac{1}{\Pi}}$

Cites Work

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