Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2017.02.11
  • Accepted : 2017.09.05
  • Published : 2018.01.01
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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.

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References

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