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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 μ are obtained which guarantee that the Mittag-Leffler functions E ρ (z,μ) have only negative and simple zeros under the condition 0·4ρ<0·5. An example is presented that shows that the result cannot be considerably enhanced.
MSC:
30C15Zeros of polynomials, etc. (one complex variable)
33E12Mittag-Leffler functions and generalizations