NEW SERIES IDENTITIES FOR ${\frac{1}{\Pi}}$

DOI10.4134/CKMS.c160194zbMath1382.33005OpenAlexW2805439990MaRDI QIDQ4605413

Arjun K. Rathie, Medhat A. Rakha, Mohammed Awad, Asmaa O. Mohammed

Publication date: 22 February 2018

Full work available at URL: http://www.ndsl.kr/soc_img/society/kms/DBSHCJ/2017/v32n4/DBSHCJ_2017_v32n4_865.pdf

zbMATH Keywords

Watson's theoremWhipple's theoremhypergeometric summation theoremsRamanujan series for \(\frac{1}{\Pi}\)

Mathematics Subject Classification ID

Other hypergeometric functions and integrals in several variables (33C70) Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Cites Work

• Extensions of certain classical summation theorems for the series \(_2F_1\), \(_3F_2\) and with applications in Ramanujan's summations
• \(\pi\)-formulas with free parameters
• Multisection method and further formulae for \(\pi\)
• A generalization of Kummer's identity.
• Generalizations of Whipple's theorem on the sum of a \({}_ 3 F_ 2\)
• Hypergeometric identities for 10 extended Ramanujan-type series
• Two hypergeometric summation theorems and Ramanujan-type series
• Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae
• Generalizations of classical summation theorems for the series₂F₁and₃F₂with applications
• On the rapid computation of various polylogarithmic constants
• GAUSS SUMMATION AND RAMANUJAN-TYPE SERIES FOR 1/π
• π AND OTHER FORMULAE IMPLIED BY HYPERGEOMETRIC SUMMATION THEOREMS
• More Formulas for π
• Generalizations of Dixon's Theorem on the Sum of A 3 F 2
• A Simple Formula for &#960
• Common extension of the Watson and Whipple sums and Ramanujan-likeπ-formulae
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