Alternating Euler sums at the negative integers.Article
Authors: Khristo Boyadzhiev 1,2; H. Gopalkrishna Gadiyar 3; R Padma 3
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Khristo Boyadzhiev;H. Gopalkrishna Gadiyar;R Padma
- 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.
Volume: Volume 32 - 2009
Published on: January 1, 2009
Imported on: March 3, 2015
Keywords: [MATH]Mathematics [math], [en] Euler-Boole formula, Euler sum, Hankel contour integration, Bernoulli number, Euler Polynomial, Euler-Maclaurin summation formula, Dirichlet series, Riemann zeta function