A note on the location of poles of meromorphic functions

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Kalyani, P.O.:Kalyani, Dist.:Nadia, Pin:741235, West Bengal, India.

2 Department of Mathematics, Dumkal College, P.O: Basantapur, P.S:Dumkal, Dist.:Murshidabad, Pin: 742406, West Bengal, India.

Abstract

A meromorphic function on an open set D contained in the finite complex plane C is of the form of the ratio between
two analytic functions defined on D with denominator not identically zero. Poles of meromorphic functions are those zeros of the denominator where numerator does not vanish. Finding all poles of a meromorphic function is too much difficult. So, it is desirable to know a region where these poles lie. In the paper we derive a region containing all the poles of some meromorphic functions. A few examples with related figures are given here to validate the results obtained.

Keywords

References

[1] A. Aziz and Q.G. Mohammad, On the zeros of a certain class of polynomialsand related analytic functions, J. Math. Anal. Appl., 1980; 75 (1980), 495502.
[2] A. Aziz and Q.G. Mohammad, Zero-free regions for polynomials and some generalizations of Enestrom-Kakeya theorem, Can. Math. Bull., 27(3) (1984), 265272.
[3] A. Aziz and W.M. Shah, On the zeros of polynomials and related analytic functions, Glasnik Matematicki, 33(53) (1998), 173-184.
[4] A. Aziz and B.A. Zargar, Bounds for the zeros of a polynomial with restricted coefficients, Applied Mathematics, 3(2012), 30-33.
[5] A. Chattopadhyay, S. Das, V.K. Jain and H. Konwar, Certain generalizations of Enestron-Kakeya theorem, Journal of Indian Mathematical Society, 72(1-4) (2005), 147-156.
[6] Y. Choo, Contributions to the zeros of a polynomial, Int. J. Math. Anal., 9 (2015), 15711577.
[7] N.K. Govil and Q.I. Rahaman, On the Enestrom-Kakeya theorem, Tohoku Math. J., 20(1968), 126-136.
[8] R. Gardner and N.K. Govil, Enestrom- Kakeya theorem and some of its generalization, Birkhauser, New Delhi, 2014. A note on the location of poles of meromorphic functions 149
[9] A. Joyal, G. Labelle and Q.I. Rahaman, On the location of zeros of polynomials, Canad. Math.Bull., 10 (1967), 53-63.
[10] V.K. Jain, On the location of zeros of polynomials, Ann. Univ. Mariae Curie-Sklodowska, Lublin-Polonia Sect. A, 30 (1976), 43-48.
[11] V.K. Jain, On Cauchy's bound for zeros of a polynomial, Turk. J. Math., 30(1) (2006), 95-100.
[12] M. Marden, Geometry of polynomials, Math. Surveys. no. 3. Amer. Math. Society., Providence, 1966.
[13] W.K. Hayman, Meromorphic functions, The Clarendon Press, Oxford, 1964.
[14] V. Valiron, Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.
Journal of Hyperstructures
Volume 10, Issue 2
December 2021
Pages 137-149

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