Solving some q-trigonometric conjectures of Gosper

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:460

Article

关键词: q-trigonometric functions;    Elliptic functions;    Theta function identities;   

DOI  :  10.1016/j.jmaa.2017.12.016

来源: Elsevier

【 摘 要 】

Gosper in 2001 introduced the functions sin(q)z and cos(q)z as q-analogues for the trigonometric functions sin z and cos z respectively. He stated, but did not prove, many identities involving the functions sin(q)z and cos(q)z along with some other related functions and constants. In this note we shall provide proofs for some of these identities by means of the classical theory of elliptic functions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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