|
This article is cited in 28 scientific papers (total in 28 papers)
On Zeros of Functions of Mittag-Leffler Type
A. M. Sedletskii M. V. Lomonosov Moscow State University
Abstract:
As is well known, the asymptotics of zeros of functions of Mittag-Leffler type
$$
E_\rho(z;\mu)=\sum_{n=0}^\infty\frac{z^n}{\Gamma(\mu+n/\rho)},\qquad\rho>0,\quad\mu\in\mathbb C,
$$
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 $E_\rho(z;\mu)$ that agrees with the asymptotics. We study the problem of the distribution of zeros of two functions that can be expressed in terms of $E_1(z;\mu)$, namely of the incomplete gamma-function and of the error function.
Received: 14.09.1999
Citation:
A. M. Sedletskii, “On Zeros of Functions of Mittag-Leffler Type”, Mat. Zametki, 68:5 (2000), 710–724; Math. Notes, 68:5 (2000), 602–613
Linking options:
https://www.mathnet.ru/eng/mzm992https://doi.org/10.4213/mzm992 https://www.mathnet.ru/eng/mzm/v68/i5/p710
|
|