Skip to main content
SpringerLink
Log in

A generalization of Laguerre's theorems on zeros of entire functions

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We prove some results generalizing the classical Laguerre theorems about the multiplicity and the number of zeros of the function

$$\sum\limits_{n = 0}^\infty {\varphi (n)\frac{{f^{(n)} (0)}}{{n!}}} z^n .$$

Some specific applications are given.

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. E. Titchmarsh,The Theory of Functions, Oxford University Press, Oxford (1939).

    Google Scholar 

  2. B. Ya. Levin,Distribution of Roots of Entire Functions [in Russian], Gostekhizdat, Moscow (1956).

    Google Scholar 

  3. Yu. A. Kaz'min, “On a problem of Gel'fond-Ibragimov. II,”Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.], No. 6, 37–44 (1965).

    MATH  Google Scholar 

  4. G. Pólya and G. Szegö,Aufgaben und Lehrsätze aus der Analysis. Bd. 2, Springer, Berlin (1925).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ural Scientific Center of the Russian Academy of Sciences, Ufa

    S. G. Merzlyakov

Authors
  1. S. G. Merzlyakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 855–863, June, 1997.

Translated by V. E. Nazaikinskii

Rights and permissions

Reprints and permissions

About this article

Cite this article

Merzlyakov, S.G. A generalization of Laguerre's theorems on zeros of entire functions. Math Notes 61, 717–723 (1997). https://doi.org/10.1007/BF02361213

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02361213

Key words

Search

Navigation