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]
Zheltukhina, Natalya1
1 Department of Mathematics, Bilkent University, 06533 Bilkent, Ankara, Turkey
Comptes Rendus. Mathématique, Tome 335 (2002) no. 2, pp. 133-138.

On étudie la distribution asymptotique (quand n→∞) des zéros de (1−λ)sn(z)−λtn+1(z), où λ∈ℂ, sn est la nème section, tn est le nème reste du developpement de la fonction de Mittag–Leffler E1/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)sn(z)−λtn+1(z), where λ∈ℂ, sn is nth section, tn is nth tail of the power series of Mittag–Leffler function E1/ρ of order ρ>1. Our results generalize the results by Edrei, Saff and Varga for the case λ=0.

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Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02442-1
Zheltukhina, Natalya 1

1 Department of Mathematics, Bilkent University, 06533 Bilkent, Ankara, Turkey 
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Zheltukhina, Natalya. Asymptotic zero distribution of sections and tails of Mittag–Leffler functions. Comptes Rendus. Mathématique, Tome 335 (2002) no. 2, pp. 133-138. doi : 10.1016/S1631-073X(02)02442-1. http://www.numdam.org/articles/10.1016/S1631-073X(02)02442-1/

[1] Buckholtz, J.D. A characteriation of the exponential series, Part II, Amer. Math. Monthly, Volume 73 (1966), pp. 121-123

[2] Carpenter, A.J.; Varga, R.S.; Waldvogel, J. Asymptotics for the partial sums of ez, I, Rocky Mountain J. Math., Volume 21 (1991) no. 1, pp. 99-120

[3] Dieudonné, J. Sur les zéros des polynomes-sections de ex, Bull Soc. Math. France, Volume 70 (1935), pp. 333-351

[4] Djrbashian, M.M. Integral Transforms and Representations of Functions in the Complex Domain, Nauka, Moskow, 1966 (in Russian)

[5] Edrei, A.; Saff, E.B.; Varga, R.S. Zeros of sections of power series, Lecture Notes in Math., 1002, 1983, pp. 1-115

[6] Ostrovskii, I.V. On zero distribution of sections and tails of power series, Israel Math. Conf. Proc., Volume 15 (2001), pp. 297-310

[7] Pólya, G.; Szegö, G. Problems and Theorems in Analysis, I, Springer-Verlag, Berlin, 1976

[8] Pólya, G.; Szegö, G. Problems and Theorems in Analysis, II, Springer-Verlag, Berlin, 1976

[9] Newman, D.J.; Rivlin, T.J. The zeros of the partial sums of the exponential function, J. Approx. Theory, Volume 5 (1972), pp. 405-412

[10] Szegö, G. Über eine Eigenschaft der Exponentialreihe, Sitzungsber. Berliner Math. Gesellsch., Volume 23 (1924), pp. 50-64

[11] Yıldırım, C.Y. A sum over the zeros of partial sums of ez, J. Ramanujan Math. Soc., Volume 6 (1991) no. 1, 2, pp. 51-66

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