caa a22 4500 475740912 CHVBK 20180406123459.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1026671508108 doi (NATIONALLICENCE)springer-10.1023/A:1026671508108 Sedletskii A. M. V. Lomonosov Moscow State University, Russia aut On Zeros of Functions of Mittag--Leffler Type [Elektronische Daten] [A. Sedletskii] As is well known, the asymptotics of zeros of functions of Mittag--Leffler type $$E_\rho \left( {z;\mu } \right) = \sum\limits_{n = 0}^\infty {\frac{{z^n }}{{\Gamma \left( {\mu + {n \mathord{\left/ {\vphantom {n \rho }} \right. \kern-\nulldelimiterspace} \rho }} \right)}}} ,{\text{ }}\rho >0,{\text{ }}\mu \in \mathbb{C},$$ describes the behavior of zeros outside a disk of sufficiently large radius. In the paper we solve the problem of finding the number of zeros inside such a disk; this allows us to indicate the numeration of all zeros $$E_\rho \left( {z;\mu } \right)$$ that agrees with the asymptotics. We study the problem of the distribution of zeros of two functions that can be expressed in terms of $$E_1 \left( {z;\mu } \right)$$ , namely of the incomplete gamma-function and of the error function. Plenum Publishing Corporation, 2000 Mittag--Leffler function nationallicence zeros of an entire function nationallicence incomplete gamma-function nationallicence error function nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 602-613 0001-4346 68:5-6<602 2000 68 11006 https://doi.org/10.1023/A:1026671508108 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1026671508108 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sedletskii A. M. V. Lomonosov Moscow State University, Russia aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 68/5-6(2000-11-01), 602-613 0001-4346 68:5-6<602 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer