Turkish Journal of Mathematics
Abstract
In this paper, using the Boole summation formula, we obtain a new integral representation of $n$-th quasi-periodic Euler functions $\overline{E}_n(x)$ for $n=1,2,\ldots.$ We also prove several series involving Euler zeta functions $\zeta_{E}(s),$ which are analogues of the corresponding results by Apostol on some series involving the Riemann zeta function $\zeta(s).$
DOI
10.3906/mat-1704-107
Keywords
Hurwitz-type Euler zeta functions, Euler zeta functions, Euler polynomials, Boole summation formula, quasi-periodic Euler functions
First Page
1166
Last Page
1179
Recommended Citation
KIM, M (2018). Some series involving the Euler zeta function. Turkish Journal of Mathematics 42 (3): 1166-1179. https://doi.org/10.3906/mat-1704-107
