Asymptotic zero distribution of sections and tails of Mittag–Leffler functions

Natalya Zheltukhina

doi:10.1016/S1631-073X(02)02442-1

Asymptotic zero distribution of sections and tails of Mittag–Leffler functions
[Distribution asymptotique des zéros pour les sections et les restes des fonctions de Mittag–Leffler]

Natalya Zheltukhina ¹

¹ Department of Mathematics, Bilkent University, 06533 Bilkent, Ankara, Turkey

Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 133-138.

Résumé
Abstract

On étudie la distribution asymptotique (quand n→∞) des zéros de (1−λ)s_n(z)−λt_n+1(z), où $λ \in ℂ$ , s_n est la nème section, t_n est le nème reste du developpement de la fonction de Mittag–Leffler E_1/ρ d'ordre ρ>1. On généralise les résultats obtenus par Edrei, Saff et Varga dans le cas λ=0.

We study the asymptotic (as n→∞) zéro distribution of (1−λ)s_n(z)−λt_n+1(z), where $λ \in ℂ$ , s_n is nth section, t_n is nth tail of the power series of Mittag–Leffler function E_1/ρ of order ρ>1. Our results generalize the results by Edrei, Saff and Varga for the case λ=0.

Reçu le : 2002-05-06
Accepté le : 2002-05-13
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02442-1

Affiliations des auteurs :

Natalya Zheltukhina ¹

¹ Department of Mathematics, Bilkent University, 06533 Bilkent, Ankara, Turkey

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     author = {Natalya Zheltukhina},
     title = {Asymptotic zero distribution of sections and tails of {Mittag{\textendash}Leffler} functions},
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     pages = {133--138},
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Natalya Zheltukhina. Asymptotic zero distribution of sections and tails of Mittag–Leffler functions. Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 133-138. doi : 10.1016/S1631-073X(02)02442-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02442-1/

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