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About the zeros of some entire functions and their derivatives

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

Todor Stoyanov
Todor Stoyanov
Affiliation:
Economic University Department of Mathematics bul. Knyaz Boris I 77 Varna 9002 Bulgaria
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Abstract

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In this article we localize the zeros of some polynomials and the derivatives of some entire functions of finite genus. If we put m = 1 in the condition of Theorem 1 we obtain the famous Obreshkoff Theorem which can be regarded as a ‘complex version’ of a well-known theorem due to Laguerre. The nonreal zeros of the derivative of the real entire funtion of Theorem 3 must belong to circles Vk which are similar to the Jen circles for polynomials.

MSC classification

Secondary: 30D20: Entire functions, general theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 2 , April 2000 , pp. 165 - 169
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Pólya, G. and Szegö, G., Problems and theorems in analysis I (Springer, Berlin, 1972).Google Scholar
[2]Stoyanov, T., ‘Some extensions of Rolle's and Gauss-Lucas theorems’, in: Second international workshop transform methods and special functions (Varna, 08 23–30, 1996).Google Scholar
[3]Titchmarsh, E. C., The theory of functions (Oxford Univ. Press, London, 1939).Google Scholar