Special values and integral representations for the Hurwitz-type Euler zeta functions

2015/08/17 by Su Hu, Daeyeoul Kim, Hu, Su +3 · 1 citation
Mathematics · #11B68 #11M35 #33B15 #33E20 #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1508.04084

openalex publication_date 2015/08/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The Hurwitz-type Euler zeta function is defined as a deformation of the Hurwitz zeta function: ζ_E(s,x)=∑_n=0^∞((-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 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.

Cited by

• On the properties of alternating invariant functions

Related

• A new extension of Hurwitz-Lerch Zeta function
• On p-adic Hurwitz-type Euler zeta functions
• Simplest Integrals for the Zeta Function and its Generalizations Valid in All ℂ
• A few remarks on values of Hurwitz Zeta function at natural and rational arguments
• A note on the Hurwitz-Lerch zeta function