Special functions related to Dedekind-type DC-sums and their applications
By Yilmaz Simsek. 2009
90 citations recorded by the source corpus.
In this paper, we construct trigonometric functions in the form of a sum Tp(h, k) which is referred to as a Dedekind-type DC-(Dahee and Changhee) sum. We establish analytic properties of this sum, find its trigonometric representations, and prove a reciprocity theorem for these sums. Furthermore, we obtain relationships between the Clausen functions, polylogarithm function, Hurwitz zeta function, generalized Lambert series (G-series), Hardy-Berndt sums, and the sum Tp(h, k). We also give some applications related to these sums and functions.
Subfields: Algebra and Number Theory, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/121d5c68f494935239fdac12b4eb9241fa4f560c
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In Algebra and Number Theory
- Yilmaz Simsek
- Taekyun Kim
- Veli Kurt
- Hari M. Srivastava
- Daeyeoul Kim
- Qiu-Ming Luo
- I. N. Cangul
- Hacer Ozden
In Statistical and Nonlinear Physics
Citations in the corpus
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- Computation methods for combinatorial sums and Euler‐type numbers related to new families of numbers (2016, background): “[8, 9, 11, 21, 23]; see also the references cited in each of these earlier works).”