Applications of Zeilberger’s Algorithm to Ramanujan-Inspired Series Involving Harmonic-Type Numbers

DOI10.47443/dml.2022.050OpenAlexW4296275132MaRDI QIDQ5884260

John Maxwell Campbell

Publication date: 20 March 2023

Published in: Discrete Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.47443/dml.2022.050

zbMATH Keywords

difference equationZeilberger's algorithmcreative telescopingRamanujan-like seriesharmonic-type number

Mathematics Subject Classification ID

Additive difference equations (39A10) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items

On Mneimneh's binomial sum involving harmonic numbers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ramanujan-like series for \(\frac{1}{\pi}\) involving harmonic numbers
• Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients
• From Wallis and Forsyth to Ramanujan
• A certain series associated with Catalan's constant
• Series with harmonic-like numbers and squared binomial coefficients
• Explicit identities for infinite families of series involving squared binomial coefficients
• Harmonic-binomial Euler-like sums via expansions of \((\arcsin x)^p\)
• New series involving harmonic numbers and squared central binomial coefficients
• Identities for Catalan's constant arising from integrals depending on a parameter
• A Wilf–Zeilberger–Based Solution to the Basel Problem With Applications