The authors have obtained some nonasymptotic results on the distribution of zeros of the function
which is a generalization of the classical Mittag-Leffler function. One of the main results of the article is contained in the following theorem.
Theorem. Assume that one of the following conditions is satisfied:
(i) , ; (ii) , ; (iii) , .
Then all zeros of are situated outside the angle .
The set : all zeros of are negative and simple} has been investigated in the article and as a corollary the generalization of Wiman’s theorem has been proved:
If , then all zeros of both and are negative and simple.