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P. Borwein, “The Arc Length of the Lemniscate {|p(z)| = 1},” Proceedings of the AMS—American Mathematical Society, Vol. 123, 1995, pp. 797-799.

has been cited by the following article:

• TITLE: On the Growth and Polynomial Coefficients of Entire Series

  AUTHORS: Huzoor H. Khan, Rifaqat Ali

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

  JOURNAL NAME: Applied Mathematics, Vol.2 No.9, September 19, 2011

  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.