![](/images/graphics-bg.png)
Euler Numbers and Polynomials Associated with Zeta Functions
Author
Source
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-04-21
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
For s∈ℂ, the Euler zeta function and the Hurwitz-type Euler zeta function are defined by ζE(s)=2∑n=1∞((−1)n/ns), and ζE(s,x)=2∑n=0∞((−1)n/(n+x)s).
Thus, we note that the Euler zeta functions are entire functions in whole complex s-plane, and these zeta functions have the values of the Euler numbers or the Euler polynomials at negative integers.
That is, ζE(−k)=Ek∗, and ζE(−k,x)=Ek∗(x).
We give some interesting identities between the Euler numbers and the zeta functions.
Finally, we will give the new values of the Euler zeta function at positive even integers.
American Psychological Association (APA)
Kim, Taekyun. 2008. Euler Numbers and Polynomials Associated with Zeta Functions. Abstract and Applied Analysis،Vol. 2008, no. 2008, pp.1-11.
https://search.emarefa.net/detail/BIM-987605
Modern Language Association (MLA)
Kim, Taekyun. Euler Numbers and Polynomials Associated with Zeta Functions. Abstract and Applied Analysis No. 2008 (2008), pp.1-11.
https://search.emarefa.net/detail/BIM-987605
American Medical Association (AMA)
Kim, Taekyun. Euler Numbers and Polynomials Associated with Zeta Functions. Abstract and Applied Analysis. 2008. Vol. 2008, no. 2008, pp.1-11.
https://search.emarefa.net/detail/BIM-987605
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-987605