On the Gosper's \(q\)-constant \(\Pi_q\)

DOI10.1007/s10114-018-8019-4zbMath1440.11061OpenAlexW2807185451MaRDI QIDQ1633826

Mohamed El Bachraoui

Publication date: 21 December 2018

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-018-8019-4

zbMATH Keywords

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

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Holomorphic modular forms of integral weight (11F11) Automorphic forms, one variable (11F12) Elliptic functions and integrals (33E05)

Related Items (8)

On Gosper's \(\mathit{\Pi}_q\) and Lambert series identities ⋮ On \(q\)-analogues for trigonometric identities ⋮ On some \(\Pi_q\)-identities of Gosper ⋮ On certain \(q\)-trigonometric identities analogous to that of Gosper's ⋮ Proofs for certain \(\Pi_q\)-identities of W. Gosper ⋮ Proof for a \(\Pi_q\)-identity of Gosper ⋮ Proof for a \(q\)-trigonometric identity of Gosper ⋮ Modular proofs of Gosper's identities

Cites Work

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• Solving some \(q\)-trigonometric conjectures of Gosper
• 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
• Eta Products and Theta Series Identities
• 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
• Ramanujan's Lost Notebook

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