A NOTE ON THE DISTRIBUTION OF ZEROS OF POLYNOMIALS AND CERTAIN CLASS OF TRANSCENDENTAL ENTIRE FUNCTIONS


By

Sanjib Kumar Datta1 and Tanchar Molla2

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

2Department of Mathematics, Dumkal College, P.O: Basantapur, P.S: Dumkal, Dist: Murshidabad- 742406, West Bengal, India Email:sanjibdatta05@gmail.com, tanumath786@gmail.com

(Received : September 04, 2021; Revised in format : September 14, 2021; Accepted : April 23, 2022)


Abstract

In the paper we wish to find a region containing all the zeros of a polynomial. Our result in some special case sharpen some very well known results obtained for this purpose. Also, we obtain a zero free region about an arbitrary point for a certain class of transcendental entire functions by restricting the coefficients of its Taylor’s series expansions to some conditions.


2020 Mathematical Sciences Classification: 30D20, 30C10, 30C15, 30D10.

Keywords and Phrases: Polynomial, transcendental entire function, coefficients, zeros, region



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