Some identities and reciprocity relationsof unipoly-Dedekind type DC sums

Journal of Inequalities and Applications

Hye Kyung Kim¹  Dae Sik Lee² 

[1] Department of Mathematics Education, Daegu Catholic University;School of Electronic and Electric Engineering, Daegu University;

关键词: Dedekind type DC sums;    Type 2 poly-Euler polynomials;    Type 2 poly-Genocchi polynomials;    Poly-Euler polynomials;    Euler function;    Polylogarithm function;   

DOI  :  10.1186/s13660-021-02655-2

来源: DOAJ

【 摘 要 】

Abstract Dedekind type DC sums and their generalizations are defined in terms of Euler functions and their generalization. Recently, Ma et al. (Adv. Differ. Equ. 2021:30 2021) introduced the poly-Dedekind type DC sums by replacing the Euler function appearing in Dedekind sums, and they were shown to satisfy a reciprocity relation. In this paper, we consider two kinds of new generalizations of the poly-Dedekind type DC sums. One is a unipoly-Dedekind type DC sum associated with the type 2 unipoly-Euler functions expressed in the type 2 unipoly-Euler polynomials using the modified polyexponential function, and we study some identities and the reciprocity relation for these unipoly-Dedekind type DC sums. The other is a unipoly-Dedekind sums type DC associated with the poly-Euler functions expressed in the unipoly-Euler polynomials using the polylogarithm function, and we derive some identities and the reciprocity relation for those unipoly-Dedekind type DC sums.

【 授权许可】

Unknown