Proof for a q-Trigonometric Identity of Gosper

被引：0
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作者：
Bing He
Fuli He
Hongcun Zhai
机构：
[1] Central South University,School of Mathematics and Statistics
[2] Luoyang Normal University,Department of Mathematics
来源：
Mediterranean Journal of Mathematics | 2020年 / 17卷
关键词：
-Trigonometric identity; Riemann’s addition formula; Jacobi theta function; Ptolemy’s theorem; 11F27; 33E05; 11E25;
D O I：
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摘要：
Gosper in 2001 introduced the q-trigonometric functions and conjectured many interesting q-trigonometric identities. In this paper, we apply Riemann’s addition formula to deduce two Jacobi theta function identities. From these theta function identities, we confirm a q-trigonometric identity conjectured by Gosper and establish two other similar results. As an application, two theta function analogues for Ptolemy’s theorem are given.
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