An accurate approximation of zeta-generalized-Euler-constant functions

Vito Lampret

Vito Lampret

Open Mathematics, Tome 8 (2010), p. 488-499 / Harvested from The Polish Digital Mathematics Library

Résumé

Zeta-generalized-Euler-constant functions, $γ (s) : = \sum_{k = 1}^{\infty} (\frac{1}{k^{s}} - \int_{k}^{k + 1} \frac{d x}{x^{s}})$ and $\tilde{γ} (s) : = \sum_{k = 1}^{\infty} {(- 1)}^{k + 1} (\frac{1}{k^{s}} - \int_{k}^{k + 1} \frac{d x}{x^{s}})$ defined on the closed interval [0, ∞), where γ(1) is the Euler-Mascheroni constant and $\tilde{γ}$ (1) = ln $\frac{4}{π}$ , are studied and estimated with high accuracy.

Publié le : 2010-01-01

Zbl 1204.33027

EUDML-ID : urn:eudml:doc:269603

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     author = {Vito Lampret},
     title = {An accurate approximation of zeta-generalized-Euler-constant functions},
     journal = {Open Mathematics},
     volume = {8},
     year = {2010},
     pages = {488-499},
     zbl = {1204.33027},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0030-7}
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Vito Lampret. An accurate approximation of zeta-generalized-Euler-constant functions. Open Mathematics, Tome 8 (2010) pp. 488-499. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0030-7/

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