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On the Growth and Polynomial Coefficients of Entire Series
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Applied Mathematics·Volume 02 (2011)·Pages 1124–1128·Published 29 September 2011·DOI10.4236/am.2011.29155
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Abstract
In this paper we have generalized some results of Rahman [1] by considering the maximum of |<i>f(z)</i>| over a certain lemniscate instead of considering the maximum of|<i>f(z)</i>|, for |<i>z</i>|=<i>r</i> and obtain the analogous results for the entire function |<i>f(z)</i>|=Σ<i>p<sub>k</sub></i>(<i>z</i>) [<i>q(z)</i>]<sup>k-1</sup> where <i>q(z)</i> is a polynomial of degree <i>m</i> and <i>p<sub>k</sub>(z)</i>is of degree <i>m</i>-1. Moreover, we have obtained some inequalities on the lover order, type and lower type in terms of polynomial coefficients.
KeywordsLemniscateLower OrderLower TypeSlowly Changing FunctionPolynomial Coefficients and Entire Functions.
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