- Gazi University Journal of Science Part A: Engineering and Innovation
- Vol: 10 Issue: 2
- Identities for a Special Finite Sum Related to the Dedekind Sums and Fibonacci Numbers
Identities for a Special Finite Sum Related to the Dedekind Sums and Fibonacci Numbers
Authors : Elif Çetin
Pages : 232-240
Doi:10.54287/gujsa.1280707
View : 34 | Download : 29
Publication Date : 2023-06-27
Article Type : Research Article
Abstract :The origin of this article is to achieve original equations related to the special finite sum C(μ,β;1), which is connected with Dedekind, Hardy, Simsek, and many other finite sums. By using the analytic properties of this sum, many useful identities are established between the C(μ,β;1) sum and other well-known finite sums. Through the use of these identities, the reciprocity law of this sum is obtained. Furthermore, another reciprocity law of the sum C(μ,β;1) is presented for μ and β are particular Fibonacci numbers. This remarkable result establishes a connection between number theory and analysis.Keywords : Hardy Sums, Dedekind Sums, Simsek Sums, Fibonacci Numbers