Asymptotic behavior of zeros of Mittag-Leffler functions of order 1/2

Let z _n denote the sequence of zeros of the Mittag-Leffler function E _ρ (z; μ), ρ > 0, μ ∈ ?, which is an entire function of order ρ. With the exception of the case ρ = 1/2, Re μ = 3 an asymptotic behavior of the sequence z _n ^ρ was known earlier up to infinitesimals o(1) having a sharply defined rate of decrease. In this paper the behavior of the sequence z _n ^1/2 is studied just in this exceptional case. Furthermore, for ρ = 1/2, μ > 3 we give the form of a curvilinear half-plane which is free of the points z _n .