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On the Growth and Polynomial Coefficients of Entire Series

On the Growth and Polynomial Coefficients of Entire Series
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摘要 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. 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.
机构地区 不详
出处 《Applied Mathematics》 2011年第9期1124-1128,共5页 应用数学(英文)
关键词 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.
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