• Title/Summary/Keyword: transcendental entire function

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MAXIMUM CURVES OF TRANSCENDENTAL ENTIRE FUNCTIONS OF THE FORM $E^{p(z)}$

  • Kim, Jeong-Heon;Kim, Youn-Ouck;Kim, Mi-Hwa
    • Journal of applied mathematics & informatics
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    • v.29 no.1_2
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    • pp.451-457
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    • 2011
  • The function f(z) = $e^{p(z)}$ where p(z) is a polynomial of degree n has 2n Julia lines. Julia lines of $e^{p(z)}$ divide the complex plane into 2n equal sectors with the same vertex at the origin. In each sector, $e^{p(z)}$ has radial limits of 0 or innity. Main results of the paper are concerned with maximum curves of $e^{p(z)}$. We deal with some properties of maximum curves of $e^{p(z)}$ and we give some examples of the maximum curves of functions of the form $e^{p(z)}$.

Meromorphic Functions Sharing a Nonzero Value with their Derivatives

  • Li, Xiao-Min;Ullah, Rahman;Piao, Da-Xiong;Yi, Hong-Xun
    • Kyungpook Mathematical Journal
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    • v.55 no.1
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    • pp.137-147
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    • 2015
  • Let f be a transcendental meromorphic function of finite order in the plane such that $f^{(m)}$ has finitely many zeros for some positive integer $m{\geq}2$. Suppose that $f^{(k)}$ and f share a CM, where $k{\geq}1$ is a positive integer, $a{\neq}0$ is a finite complex value. Then f is an entire function such that $f^{(k)}-a=c(f-a)$, where $c{\neq}0$ is a nonzero constant. The results in this paper are concerning a conjecture of Bruck [5]. An example is provided to show that the results in this paper, in a sense, are the best possible.