Special values and integral representations for the hurwitz-type euler zeta functions

Su Hu; Daeyeoul Kim; Min Soo Kim

doi:10.4134/JKMS.j170110

Special values and integral representations for the hurwitz-type euler zeta functions

Su Hu
, Daeyeoul Kim
, Min Soo Kim

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

12 Scopus citations

Abstract

The Hurwitz-type Euler zeta function is defined as a deformation of the Hurwitz zeta function: (Forumala Presented). In this paper, by using the method of Fourier expansions, we shall evaluate several integrals with integrands involving Hurwitz-type Euler zeta functions ζ_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.

Original language	English
Pages (from-to)	185-210
Number of pages	26
Journal	Journal of the Korean Mathematical Society
Volume	55
Issue number	1
DOIs	https://doi.org/10.4134/JKMS.j170110
State	Published - 2018

Keywords

Euler polynomials
Fourier series
Hurwitz zeta functions
Integrals

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.4134/JKMS.j170110

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title = "Special values and integral representations for the hurwitz-type euler zeta functions",

abstract = "The Hurwitz-type Euler zeta function is defined as a deformation of the Hurwitz zeta function: (Forumala Presented). In this paper, by using the method of Fourier expansions, we shall evaluate several integrals with integrands involving Hurwitz-type Euler zeta functions ζE(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 = "Euler polynomials, Fourier series, Hurwitz zeta functions, Integrals",

author = "Su Hu and Daeyeoul Kim and Kim, \{Min Soo\}",

note = "Publisher Copyright: {\textcopyright} 2018 Korean Mathematical Society.",

year = "2018",

doi = "10.4134/JKMS.j170110",

language = "English",

volume = "55",

pages = "185--210",

journal = "Journal of the Korean Mathematical Society",

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T1 - Special values and integral representations for the hurwitz-type euler zeta functions

AU - Hu, Su

AU - Kim, Daeyeoul

AU - Kim, Min Soo

PY - 2018

Y1 - 2018

N2 - The Hurwitz-type Euler zeta function is defined as a deformation of the Hurwitz zeta function: (Forumala Presented). In this paper, by using the method of Fourier expansions, we shall evaluate several integrals with integrands involving Hurwitz-type Euler zeta functions ζE(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.

AB - The Hurwitz-type Euler zeta function is defined as a deformation of the Hurwitz zeta function: (Forumala Presented). In this paper, by using the method of Fourier expansions, we shall evaluate several integrals with integrands involving Hurwitz-type Euler zeta functions ζE(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.

KW - Euler polynomials

KW - Fourier series

KW - Hurwitz zeta functions

KW - Integrals

UR - https://www.scopus.com/pages/publications/85039794543

U2 - 10.4134/JKMS.j170110

DO - 10.4134/JKMS.j170110

M3 - Journal article

AN - SCOPUS:85039794543

SN - 0304-9914

VL - 55

SP - 185

EP - 210

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 1

ER -

Special values and integral representations for the hurwitz-type euler zeta functions

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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