On the Growth and Polynomial Coefficients of Entire Series

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)*|=Σ*p*_{k}(*z*) [*q(z)*]^{k-1} where *q(z)* is a polynomial of degree *m* and *p*_{k}(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.

In this paper we have generalized some results of Rahman [1] by considering the maximum of |

Keywords

Lemniscate, Lower Order, Lower Type, Slowly Changing Function, Polynomial Coefficients and Entire Functions.

Lemniscate, Lower Order, Lower Type, Slowly Changing Function, Polynomial Coefficients and Entire Functions.

Cite this paper

nullH. Khan and R. Ali, "On the Growth and Polynomial Coefficients of Entire Series,"*Applied Mathematics*, Vol. 2 No. 9, 2011, pp. 1124-1128. doi: 10.4236/am.2011.29155.

nullH. Khan and R. Ali, "On the Growth and Polynomial Coefficients of Entire Series,"

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