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

100%

Lampret V.

Open Mathematics

2010

tom 8

nr 3

488-499

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.

Accelerating the convergence of trigonometric series

100%

Nersessian A., Poghosyan A.

Open Mathematics

2006

tom 4

nr 3

435-448

A nonlinear method of accelerating both the convergence of Fourier series and trigonometric interpolation is investigated. Asymptotic estimates of errors are derived for smooth functions. Numerical results are represented and discussed.

Ograniczanie wyników

2 Open Mathematics

1 Lampret V.

1 Nersessian A.

1 Poghosyan A.

1 2010

1 2006

Wyniki wyszukiwania

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

Accelerating the convergence of trigonometric series