Alternating Euler sums at the negative integers.

Khristo Boyadzhiev; H. Gopalkrishna Gadiyar; R Padma

doi:10.46298/hrj.2009.165

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

hrj:165 - Hardy-Ramanujan Journal, January 1, 2009, Volume 32 - 2009 - https://doi.org/10.46298/hrj.2009.165

Alternating Euler sums at the negative integers.Article

Authors: Khristo Boyadzhiev ^1,²; H. Gopalkrishna Gadiyar ³; R Padma ³

1 Mathematics Department, The Ohio State University
2 Department of Mathematics [Ohio State University]
3 KBC research Center

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.

https://doi.org/10.46298/hrj.2009.165

Source: HAL:hal-01112352v1

Volume: Volume 32 - 2009

Published on: January 1, 2009

Imported 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]

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

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