Further WZ-based methods for proving and generalizing Ramanujan's series

DOI10.1080/10236198.2023.2198042MaRDI QIDQ6044157

John Maxwell Campbell, Paul Levrie

Publication date: 17 May 2023

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

zbMATH Keywords

hypergeometric seriesWZ methodRamanujan seriesRamanujan-like series

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Evaluation of number-theoretic constants (11Y60) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Cites Work

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• Generators of some Ramanujan formulas
• On WZ-pairs which prove Ramanujan series
• Generating function identities for \(\zeta (2n+2)\), \(\zeta (2n+3)\) via the WZ method
• From Wallis and Forsyth to Ramanujan
• Some binomial series obtained by the WZ-method
• Hypergeometric identities for 10 extended Ramanujan-type series
• WZ-Proofs of “Divergent” Ramanujan-Type Series
• Rational Functions Certify Combinatorial Identities
• WZ pairs and q-analogues of Ramanujan series for 1/π
• A WZ proof for a Ramanujan-like series involving cubed binomial coefficients
• Using Fourier-Legendre expansions to derive series for \(\frac{1}{\pi}\) and \(\frac{1}{\pi^{2}}\)

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