TY - JOUR
T1 - Proofs for two q-trigonometric identities of Gosper
AU - Abo Touk, Sarah
AU - Al Houchan, Zina
AU - El Bachraoui, Mohamed
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - In 2001, Gosper introduced q-analogues for the functions sinz and cosz and stated without proofs many identities involving these q-analogues. Gosper asked whether his formulas are true. In this paper, we shall use the theory of elliptic functions to confirm two of Gosper's identities. Moreover, we shall give two consequences of these identities.
AB - In 2001, Gosper introduced q-analogues for the functions sinz and cosz and stated without proofs many identities involving these q-analogues. Gosper asked whether his formulas are true. In this paper, we shall use the theory of elliptic functions to confirm two of Gosper's identities. Moreover, we shall give two consequences of these identities.
KW - Elliptic functions
KW - Theta function identities
KW - q-Trigonometric functions
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U2 - 10.1016/j.jmaa.2017.07.030
DO - 10.1016/j.jmaa.2017.07.030
M3 - Article
AN - SCOPUS:85025833664
SN - 0022-247X
VL - 456
SP - 662
EP - 670
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -