A NOTE ON SHARPENING OF A THEOREM OF ANKENY AND RIVLIN

Applicable Analysis and Discrete Mathematics

article

Aseem Dalal¹  Narendra K. Govil² 

[1] Department of Mathematics, Indian Institute of Technology Delhi;Department of Mathematics and Statistics, Auburn University

关键词: Inequalities in complex plane;    Polynomials and rational functions;    Approximation in complex plane;   

DOI  :  10.2298/AADM200206012D

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

In this paper, we sharpen the above inequality of Govil, which in turn sharpens inequality of Ankeny and Rivlin. We present our result in terms of theLerchPhi function Φ(z, s, a), implemented in Wolfram’s MATHEMATICA asLerchPhi [z, s, a], which can be evaluated to arbitrary numerical precision,and is suitable for both symbolic and numerical manipulations. Also, wepresent an example and by using MATLAB show that for some polynomialsthe improvement in bound can be considerably significant.

【 授权许可】

Unknown