Solving some \(q\)-trigonometric conjectures of Gosper

DOI10.1016/j.jmaa.2017.12.016zbMath1384.33031OpenAlexW2773996161WikidataQ123148939 ScholiaQ123148939MaRDI QIDQ681772

Mohamed El Bachraoui

Publication date: 13 February 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.12.016

zbMATH Keywords

elliptic functionstheta function identities\(q\)-trigonometric functions

Mathematics Subject Classification ID

Dedekind eta function, Dedekind sums (11F20) (q)-gamma functions, (q)-beta functions and integrals (33D05) Elliptic functions and integrals (33E05)

Related Items

On the Gosper's \(q\)-constant \(\Pi_q\) ⋮ On a theta product of Jacobi and its applications to \(q\)-gamma products ⋮ Some new sums of q-trigonometric and related functions through a theta product of Jacobi ⋮ On series identities of Gosper and integrals of Ramanujan theta function 𝜓(𝑞) ⋮ On certain trigonometric identities

Cites Work

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• An addition formula for the Jacobian theta function and its applications
• Elliptic functions and applications
• Duplication formulae involving Jacobi theta functions and Gosper’s 𝑞-trigonometric functions
• Confirming a $q$-trigonometric conjecture of Gosper
• On the Additive Formulae of the Theta Functions and a Collection of Lambert Series Pertaining to the Modular Equations of Degree 5
• A theta function identity and its implications
• On Some Modular Equations of Degree 5

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