On the Growth and Polynomial Coefficients of Entire Series

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DOI: 10.4236/am.2011.29155   PDF   HTML     3,762 Downloads   6,682 Views   Citations

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.

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H. 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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[6] J. R. Rice, “The Degree of Convergence for Entire Functions,” Duke Mathematical Journal, Vol. 38, No. 3, 1971, pp. 429-440. doi:10.1215/S0012-7094-71-03852-X
[7] O. P. Juneja, “On the Coefficients of Entire Series,” Journal of Mathematical Analysis, Vol. 24, 1971, pp. 395-401.
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[10] D. Kumar and H. Kaur, “Lp—Approximation Error and Generalized Growth Parameters of Analytic Functions in Coratheodory Domains,” International Journal of Mathematical Analysis, Vol. 3, No. 30, 2009, pp. 1461-1472.

  
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