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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Bibliographische Detailangaben
Veröffentlicht in:	Science China. Mathematics 2020-12, Vol.63 (12), p.2415-2422
Hauptverfasser:	He, Bing, Zhai, Hongcun
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Mathematics Mathematics and Statistics
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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