Some hypergeometric and other evaluations of \(\zeta (2)\) and allied series

DOI10.1016/S0096-3003(98)10082-6zbMath0965.11039OpenAlexW2026056118MaRDI QIDQ1805818

Junesang Choi, Arjun K. Rathie, Hari M. Srivastava

Publication date: 5 August 2001

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(98)10082-6

zbMATH Keywords

hypergeometric seriesRiemann zeta-functionDixon's summation theoremBasler problemGauss' summation theoremWallis' integral formulaevaluation of \(\zeta(2)\)

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Generalized hypergeometric series, ({}_pF_q) (33C20) Hurwitz and Lerch zeta functions (11M35)

Related Items

Summation and recurrence formula involving the central factorial numbers and zeta function., Some simple algorithms for the evaluations and representations of the Riemann zeta function at positive integer arguments

Cites Work

• Generalizations of Whipple's theorem on the sum of a \({}_ 3 F_ 2\)
• An Elementary Proof of ∑ ∞ n = 1 1/n 2 = π 2 /6
• The Series Σ^∞_{k = 1}k^-s, s = 2,3,4,⋯, Once More
• Generalizations of Dixon's Theorem on the Sum of A 3 F 2
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