On some expansions for the Euler Gamma function and the Riemann Zeta function |
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Authors: | Grzegorz Rza?dkowski |
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Institution: | Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University in Warsaw, Dewajtis 5, 01 - 815 Warsaw, Poland |
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Abstract: | In the present paper we introduce some expansions which use the falling factorials for the Euler Gamma function and the Riemann Zeta function. In the proofs we use the Faá di Bruno formula, Bell polynomials, potential polynomials, Mittag-Leffler polynomials, derivative polynomials and special numbers (Eulerian numbers and Stirling numbers of both kinds). We investigate the rate of convergence of the series and give some numerical examples. |
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Keywords: | 11B83 11M06 |
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