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Math. Comput. Appl. 2016, 21(3), 31; doi:10.3390/mca21030031

Analytic Properties of the Sum B1(h, k)

Department of Mathematics, Celal Bayar University, Manisa 45140, Turkey
Academic Editor: Fazal Mahomed
Received: 6 June 2016 / Revised: 12 July 2016 / Accepted: 12 July 2016 / Published: 21 July 2016
View Full-Text   |   Download PDF [723 KB, uploaded 21 July 2016]

Abstract

In this paper, with the help of the Hardy and Dedekind sums we will give many properties of the sum B 1 ( h , k ) , which was defined by Cetin et al. Then we will give the connections of this sum with the other well-known finite sums such as the Dedekind sums, the Hardy sums, the Simsek sums Y ( h , k ) and the sum C 1 ( h , k ) . By using the Fibonacci numbers and two-term polynomial relation, we will also give a new property of the sum B 1 ( h , k ) . View Full-Text
Keywords: Hardy sums; Dedekind sums; two-term polynomial relation; greatest integer function; Y(h, k) sums; C1(h, k) sums; B1(h, k) sums Hardy sums; Dedekind sums; two-term polynomial relation; greatest integer function; Y(h, k) sums; C1(h, k) sums; B1(h, k) sums
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Cetin, E. Analytic Properties of the Sum B1(h, k). Math. Comput. Appl. 2016, 21, 31.

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