Sharp inequalities related to Gosper's formula

Cristinel Mortici

doi:10.1016/j.crma.2009.12.016

Mathematical Analysis/Numerical Analysis

Sharp inequalities related to Gosper's formula
[Inégalités précises liées à la formule de Gosper]

Présenté par : Jean-Pierre Kahane

Cristinel Mortici ¹

¹ Valahia University of Târgovişte, Department of Mathematics, Bd. Unirii 18, 130082 Târgovişte, Romania

Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 137-140.

Résumé
Abstract

Le but de cette Note est de construire un nouveau type de série de Stirling, étendant la formule de Gosper pour les grandes factorielles. Nous établissons de nouvelles inégalités précises pour les fonctions gamma et digamma. Enfin, nous indiquons des calculs numériques qui démontre la supériorité de notre nouvelle série sur la série classique de Stirling.

The purpose of this Note is to construct a new type of Stirling series, which extends the Gosper's formula for big factorials. New sharp inequalities for the gamma and digamma functions are established. Finally, numerical computations which demonstrate the superiority of our new series over the classical Stirling's series are given.

Reçu le : 2009-04-29
Accepté le : 2009-12-10
Publié le : 2010-02-01

DOI : 10.1016/j.crma.2009.12.016

Affiliations des auteurs :

Cristinel Mortici ¹

¹ Valahia University of Târgovişte, Department of Mathematics, Bd. Unirii 18, 130082 Târgovişte, Romania

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     author = {Cristinel Mortici},
     title = {Sharp inequalities related to {Gosper's} formula},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {137--140},
     publisher = {Elsevier},
     volume = {348},
     number = {3-4},
     year = {2010},
     doi = {10.1016/j.crma.2009.12.016},
     language = {en},
}

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Cristinel Mortici. Sharp inequalities related to Gosper's formula. Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 137-140. doi : 10.1016/j.crma.2009.12.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.12.016/

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