Proofs for certain q-trigonometric identities of Gosper

Applying an addition formula of Liu (2007), we deduce certain Jacobi theta function identities. From these results we confirm several q -trigonometric identities conjectured by Gosper (2001). Another conjectured identity on the constant Π q is also settled.

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Bibliographic Details
Published in:Science China. Mathematics 2020-12, Vol.63 (12), p.2415-2422
Main Authors: He, Bing, Zhai, Hongcun
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:Applying an addition formula of Liu (2007), we deduce certain Jacobi theta function identities. From these results we confirm several q -trigonometric identities conjectured by Gosper (2001). Another conjectured identity on the constant Π q is also settled.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-019-9555-1