Skip to main content
SpringerLink
Log in

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

  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

Let z n denote the sequence of zeros of the Mittag-Leffler function E ρ (z; μ), ρ > 0, μ ∈ ℂ, 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 ρ n was known earlier up to infinitesimals o(1) having a sharply defined rate of decrease. In this paper the behavior of the sequence z 1/2 n 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 .

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Wiman, “Über die Nullstellen der Funktionen E α (x),” Acta Math. 29, 217–234 (1905).

    Article  MathSciNet  Google Scholar 

  2. M. M. Dzhrbashyan, Integral Transforms and Representation of Functions in a Complex Domain (Nauka, Moscow, 1966) [in Russian].

    Google Scholar 

  3. A. M. Sedletskii, “Asymptotic Formulas for Zeros of Mittag-Leffler Functions,” Anal. Math. 20, 117–132 (1994).

    Article  MathSciNet  Google Scholar 

  4. Yu. V. Sidorov, M. V. Fedoruk, and M. I. Shabunin, Lectures on the Theory of Functions of a Complex Variable, (Nauka, Moscow, 1982) [in Russian].

    MATH  Google Scholar 

  5. A. I. Markushevich, Theory of Analytic Functions, Vol. 1 (Nauka, Moscow, 1967; Chelsea, 1977).

    Google Scholar 

  6. A. M. Sedletskii, “Some Non-Asymptotic Properties of the Roots of Mittag-Leffler Functions of Order 1/2,” Mathematica Montisgnigri 13, 75–81 (2001).

    MathSciNet  Google Scholar 

  7. I. V. Ostrovskii and I. N. Peresyolkova, “Nonasymptotic Results on Distribution of Zeros of the Function E ρ (z, μ),” Anal. Math. 23, 283–296 (1997).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    A. M. Sedletskii

Authors
  1. A. M. Sedletskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.M. Sedletskii, 2007, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2007, Vol. 62, No. 1, pp. 22–28.

About this article

Cite this article

Sedletskii, A.M. Asymptotic behavior of zeros of Mittag-Leffler functions of order 1/2. Moscow Univ. Math. Bull. 62, 22–28 (2007). https://doi.org/10.3103/S0027132207010056

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132207010056

Keywords

Search

Navigation