10.46298/hrj.2009.165
https://hrj.episciences.org/165
Boyadzhiev, Khristo
Khristo
Boyadzhiev
Gadiyar, H. Gopalkrishna
H. Gopalkrishna
Gadiyar
Padma, R
R
Padma
Alternating Euler sums at the negative integers.
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.
episciences.org
Riemann zeta function
Dirichlet series
Euler-Maclaurin summation formula
Euler sum
Hankel contour integration
Bernoulli number
Euler-Boole formula
Euler Polynomial
[MATH] Mathematics [math]
2015-06-12
2009-01-01
2009-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01112352v1
2804-7370
https://hrj.episciences.org/165/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 32 - 2009
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