ON GUILLERA’S -SERIES FOR

DOI10.1017/s0004972723000060MaRDI QIDQ6069301

John Maxwell Campbell

Publication date: 14 November 2023

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

zbMATH Keywords

infinite seriesWZ methodseries accelerationclosed form

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Numerical approximation and evaluation of special functions (33F05) Evaluation of number-theoretic constants (11Y60) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Cites Work

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• On a strange evaluation of the hypergeometric series by Gosper
• A new Ramanujan-like series for \(1/\pi ^{2}\)
• Generators of some Ramanujan formulas
• On WZ-pairs which prove Ramanujan series
• Dougall's \(_5F_4\) sum and the WZ algorithm
• Some binomial series obtained by the WZ-method
• Binomial sums involving Catalan numbers
• Infinite series formulae related to Gauss and Bailey \(_2F_1(\frac{1}{2})\)-sums
• Hypergeometric identities for 10 extended Ramanujan-type series
• \(\Gamma\)-evaluations of hypergeometric series
• Accelerating Dougall’s $_5F_4$-sum and infinite series involving $\pi $
• Terminating ₂𝐹₁(4)-series perturbed by two integer parameters
• A New Method to Obtain Series for 1/π and 1/π²
• Three pairs of congruences concerning sums of central binomial coefficients
• Special Values of the Hypergeometric Series
• q-Analogues of Guillera’s two series for π±2 with convergence rate 27 64

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