TITLE:
On the Growth and Polynomial Coefficients of Entire Series
AUTHORS:
Huzoor H. Khan, Rifaqat Ali
KEYWORDS:
Lemniscate, Lower Order, Lower Type, Slowly Changing Function, Polynomial Coefficients and Entire Functions.
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.9,
September
19,
2011
ABSTRACT: In this paper we have generalized some results of Rahman [1] by considering the maximum of |f(z)| over a certain lemniscate instead of considering the maximum of|f(z)|, for |z|=r and obtain the analogous results for the entire function |f(z)|=Σpk(z) [q(z)]k-1 where q(z) is a polynomial of degree m and pk(z)is of degree m-1. Moreover, we have obtained some inequalities on the lover order, type and lower type in terms of polynomial coefficients.