Special Functions Related to Dedekind Type DC-Sums and their Applications
arXiv:0902.0380 · doi:10.1134/S1061920810040114
Abstract
In this paper we construct trigonometric functions of the sum T_{p}(h,k), which is called Dedekind type DC-(Dahee and Changhee) sums. We establish analytic properties of this sum. We find trigonometric representations of this sum. We prove reciprocity theorem of this sums. Furthermore, we obtain relations between the Clausen functions, Polylogarithm function, Hurwitz zeta function, generalized Lambert series (G-series), Hardy-Berndt sums and the sum T_{p}(h,k). We also give some applications related to these sums and functions.
References in corpus (5)
- Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent
- Euler Numbers and polynomials associated with zeta functions
- q-Hardy-Berndt type sums associated with q-Genocchi type zeta and l-functions
- Integral representations of the Legendre chi function
- Sharp approximations to the Bernoulli periodic functions by trigonometric polynomials