Some series involving the Euler zeta function

Authors : Min-soo KIM

Pages : 1166-1179

View : 14 | Download : 7

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, using the Boole summation formula, we obtain a new integral representation of $n$-th quasi-periodic Euler functions $\overline{E}_ninsert ignore into journalissuearticles values(x);$ for $n=1,2,\ldots.$ We also prove several series involving Euler zeta functions $\zeta_{E}insert ignore into journalissuearticles values(s);,$ which are analogues of the corresponding results by Apostol on some series involving the Riemann zeta function $\zetainsert ignore into journalissuearticles values(s);.$
Keywords : Hurwitz type Euler zeta functions, Euler zeta functions, Euler polynomials, Boole summation formula, quasi periodic Euler functions