An accurate approximation of zeta-generalized-Euler-constant functions
Open Mathematics (2010)
- Volume: 8, Issue: 3, page 488-499
- ISSN: 2391-5455
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topVito Lampret. "An accurate approximation of zeta-generalized-Euler-constant functions." Open Mathematics 8.3 (2010): 488-499. <http://eudml.org/doc/269603>.
@article{VitoLampret2010,
abstract = {Zeta-generalized-Euler-constant functions, \[ \gamma \left( s \right): = \sum \limits \_\{k = 1\}^\infty \{\left( \{\frac\{1\}\{\{k^s \}\} - \int \_k^\{k + 1\} \{\frac\{\{dx\}\}\{\{x^s \}\}\} \} \right)\} \]
and \[ \tilde\{\gamma \}\left( s \right): = \sum \limits \_\{k = 1\}^\infty \{\left( \{ - 1\} \right)^\{k + 1\} \left( \{\frac\{1\}\{\{k^s \}\} - \int \_k^\{k + 1\} \{\frac\{\{dx\}\}\{\{x^s \}\}\} \} \right)\} \]
defined on the closed interval [0, ∞), where γ(1) is the Euler-Mascheroni constant and \[ \tilde\{\gamma \}\]
(1) = ln \[ \frac\{4\}\{\pi \} \]
, are studied and estimated with high accuracy.},
author = {Vito Lampret},
journal = {Open Mathematics},
keywords = {Alternating; Convergence acceleration; Estimate; Generalized-Euler-constant-function; Inequality; Series; Zeta; alternating; convergence acceleration; estimate; generalized-Euler-constant-function; inequality; series; zeta},
language = {eng},
number = {3},
pages = {488-499},
title = {An accurate approximation of zeta-generalized-Euler-constant functions},
url = {http://eudml.org/doc/269603},
volume = {8},
year = {2010},
}
TY - JOUR
AU - Vito Lampret
TI - An accurate approximation of zeta-generalized-Euler-constant functions
JO - Open Mathematics
PY - 2010
VL - 8
IS - 3
SP - 488
EP - 499
AB - Zeta-generalized-Euler-constant functions, \[ \gamma \left( s \right): = \sum \limits _{k = 1}^\infty {\left( {\frac{1}{{k^s }} - \int _k^{k + 1} {\frac{{dx}}{{x^s }}} } \right)} \]
and \[ \tilde{\gamma }\left( s \right): = \sum \limits _{k = 1}^\infty {\left( { - 1} \right)^{k + 1} \left( {\frac{1}{{k^s }} - \int _k^{k + 1} {\frac{{dx}}{{x^s }}} } \right)} \]
defined on the closed interval [0, ∞), where γ(1) is the Euler-Mascheroni constant and \[ \tilde{\gamma }\]
(1) = ln \[ \frac{4}{\pi } \]
, are studied and estimated with high accuracy.
LA - eng
KW - Alternating; Convergence acceleration; Estimate; Generalized-Euler-constant-function; Inequality; Series; Zeta; alternating; convergence acceleration; estimate; generalized-Euler-constant-function; inequality; series; zeta
UR - http://eudml.org/doc/269603
ER -
References
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- [8] Sondow J., Hadjicostas P., The generalized-Euler-constant function γ(z) and a generalization of Somos’s quadratic recurrence constant, J. Math. Anal. Appl., 2007, 332, 292–314 http://dx.doi.org/10.1016/j.jmaa.2006.09.081 Zbl1113.11017
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