Duplication formulae involving Jacobi theta functions and Gosper’s 𝑞-trigonometric functions

DOI10.1090/S0002-9939-2013-11576-5zbMath1277.33018OpenAlexW2166992877WikidataQ29395048 ScholiaQ29395048MaRDI QIDQ2839310

István Mezö

Publication date: 5 July 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2013-11576-5

zbMATH Keywords

theta functions\(q\)-exponential function\(q\)-sine function\(q\)-hyperbolic functions\(q\)-trigonometryduplication \(q\)-formula

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) (q)-gamma functions, (q)-beta functions and integrals (33D05) Elliptic functions and integrals (33E05)

Related Items (14)

Proofs for certain \(q\)-trigonometric identities of Gosper ⋮ On the Gosper's \(q\)-constant \(\Pi_q\) ⋮ Proofs for two \(q\)-trigonometric identities of Gosper ⋮ On a theta product of Jacobi and its applications to \(q\)-gamma products ⋮ On \(q\)-analogues for trigonometric identities ⋮ Proofs for certain \(\Pi_q\)-identities of W. Gosper ⋮ Proving some identities of Gosper on $q$-trigonometric functions ⋮ Minimal frame operator norms via minimal theta functions ⋮ Solving some \(q\)-trigonometric conjectures of Gosper ⋮ Proof for a \(q\)-trigonometric identity of Gosper ⋮ 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 ⋮ Confirming a $q$-trigonometric conjecture of Gosper

Cites Work

• On some strange summation formulas
• An introduction to basic Fourier series
• Pages from the Computer Files of R. William Gosper
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