Abstract
In this paper, we introduce a Daehee constant, the so-called q-extension of the Napier constant, and consider the Daehee formula associated with the q-extensions of trigonometric functions. That is, we derive the q-extensions of sine and cosine functions from our Daehee formula. Finally, we present the q-calculus related to the q-extensions of sine and cosine functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Kim, “Power Series and Asymptotic Series Associated with the q-Analog of the Two-Variable p-Adic L-Function,” Russ. J. Math. Phys. 12(2), 186–196 (2005).
T. Kim, “An Invariant p-Adic Integral Associated with Daehee Numbers,” Integral Transforms Spec. Funct. 13, 65–69 (2002).
T. Kim and S. H. Rim, “A Note on the q-Integral and q-Series,” Adv. Stud. Contemp. Math. 2, 37–45 (2000).
T. H. Koornwinder, “Special Functions and q-Commuting Variables,” Fields Inst. Commun. 14, 131–166 (1997).
E. Kreyszig, Advanced Engineering Mathematics, 8th ed. (John Wiley & Sons, 1999).
M. Schork, “Wards ‘Calculus of Sequences’ q-Calculus and the Limit q → 1,” Adv. Stud. Contemp. Math. 13, 131–141 (2006).
Y. Simsek, “q-Dedekind Type Sums Related to q-Zeta Function and Basic L-Series,” J. Math. Anal. Appl. 318, 333–351 (2006).
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was partially supported by Jangjeon Mathematical Society (JMS2006-12-C0007).
Rights and permissions
About this article
Cite this article
Kim, T. q-Extension of the Euler formula and trigonometric functions. Russ. J. Math. Phys. 14, 275–278 (2007). https://doi.org/10.1134/S1061920807030041
Received:
Issue Date:
DOI: https://doi.org/10.1134/S1061920807030041