On the Growth and Polynomial Coefficients of Entire Series

Huzoor H. Khan, Rifaqat Ali

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DOI: 10.4236/am.2011.29155                

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)|=Σp_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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

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