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On q-analogues for trigonometric identities

  • Sarah Abo Touk , Zina Al Houchan and Mohamed El Bachraoui EMAIL logo
From the journal Analysis

Abstract

In this paper we will give q-analogues for the Pythagorean trigonometric identity sin2z+cos2z=1 in terms of Gosper’s q-trigonometry. We shall also give new q-analogues for the duplicate trigonometric identity sin(x-y)sin(x+y)=sin2x-sin2y. Moreover, we shall give a short proof for an identity of Gosper, which was also established by Mező. The main argument of our proofs is the residue theorem applied to elliptic functions.

MSC 2010: 33E05; 11F11; 11F12

References

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Received: 2018-06-22
Revised: 2019-03-18
Accepted: 2020-04-04
Published Online: 2020-04-17
Published in Print: 2020-05-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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