Khristo Boyadzhiev ; H. Gopalkrishna Gadiyar ; R Padma - Alternating Euler sums at the negative integers.

hrj:165 - Hardy-Ramanujan Journal, January 1, 2009, Volume 32 - https://doi.org/10.46298/hrj.2009.165
Alternating Euler sums at the negative integers.

Authors: Khristo Boyadzhiev ; H. Gopalkrishna Gadiyar ; R Padma

We study three special Dirichlet series, two of them alternating, related to the Riemann zeta-function. These series are shown to have extensions to the entire complex plane and we find their values at the negative integers (or residues at poles). These values are given in terms of Bernoulli and Euler numbers.


Volume: Volume 32
Published on: January 1, 2009
Submitted on: March 3, 2015
Keywords: Riemann zeta function,Dirichlet series, Euler-Maclaurin summation formula, Euler sum, Hankel contour integration, Bernoulli number, Euler-Boole formula, Euler Polynomial,[MATH] Mathematics [math]


Share

Consultation statistics

This page has been seen 370 times.
This article's PDF has been downloaded 161 times.