On the Ostrovskii-Peresyolkova conjecture about zeros of the Mittag-Leffler functions. (English) Zbl 1117.30005
Approximation theory: asymptotical expansions. Transl. from the Russian. Moscow: Maik Nauka/Interperiodica. Proceedings of the Steklov Institute of Mathematics 2001, Suppl. 1, S167-S182 (2001).
Summary: Bounds, best to date, of the parameter are obtained which guarantee that the Mittag-Leffler functions have only negative and simple zeros under the condition . An example is presented that shows that the result cannot be considerably enhanced.
|30C15||Zeros of polynomials, etc. (one complex variable)|
|33E12||Mittag-Leffler functions and generalizations|