Proofs for certain \(q\)-trigonometric identities of Gosper

DOI10.1007/s11425-019-9555-1zbMath1469.11079OpenAlexW2990508226WikidataQ113900264 ScholiaQ113900264MaRDI QIDQ829097

Hongcun Zhai, Bing He

Publication date: 5 May 2021

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-019-9555-1

zbMATH Keywords

Jacobi theta functionaddition formula\(q\)-trigonometric identityconstant \(\Pi_q\)

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Theta series; Weil representation; theta correspondences (11F27) Elliptic functions and integrals (33E05)

Related Items (5)

On some \(\Pi_q\)-identities of Gosper ⋮ On certain \(q\)-trigonometric identities analogous to that of Gosper's ⋮ \(q\)-analogues of two Ramanujan-type supercongruences ⋮ Modular proofs of Gosper's identities ⋮ On certain trigonometric identities

Cites Work

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• An addition formula for the Jacobian theta function and its applications
• Addition formulas for Jacobi's theta functions, Dedekind's eta function, and Ramanujan's congruences
• On certain trigonometric identities
• Proofs for two \(q\)-trigonometric identities of Gosper
• Duplication formulae involving Jacobi theta functions and Gosper’s 𝑞-trigonometric functions
• Confirming a $q$-trigonometric conjecture of Gosper
• Residue theorem and theta function identities

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