Analytic Properties of the Sum B1(h, k)

Abstract

In [11], Cetin et al. defined a new special finite sum which is denoted by B 1 (h, k). In this paper, with the help of the Hardy and Dedekind sums we will give many properties of the sum B 1 (h, k). 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).

Identities for a Special Finite Sum Related to the Dedekind Sums and Fibonacci Numbers

“…This has many relations with other well known finite sums. Cetin (2016a;2016b) gave some useful properties for this sum.…”