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http://dx.doi.org/10.4134/JKMS.j170110

SPECIAL VALUES AND INTEGRAL REPRESENTATIONS FOR THE HURWITZ-TYPE EULER ZETA FUNCTIONS  

Hu, Su (Department of Mathematics South China University of Technology)
Kim, Daeyeoul (Department of Mathematics and Institute of Pure and Applied Mathematics Chonbuk National University)
Kim, Min-Soo (Division of Mathematics, Science, and Computers Kyungnam University)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.1, 2018 , pp. 185-210 More about this Journal
Abstract
The Hurwitz-type Euler zeta function is defined as a deformation of the Hurwitz zeta function: $${\zeta}_E(s,x)={\sum_{n=0}^{\infty}}{\frac{(-1)^n}{(n+x)^s}}$$. In this paper, by using the method of Fourier expansions, we shall evaluate several integrals with integrands involving Hurwitz-type Euler zeta functions ${\zeta}_E(s,x)$. Furthermore, the relations between the values of a class of the Hurwitz-type (or Lerch-type) Euler zeta functions at rational arguments have also been given.
Keywords
Hurwitz zeta functions; Euler polynomials; integrals; Fourier series;
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