• Title/Summary/Keyword: Entire function

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THE ITERATION OF ENTIRE FUNCTION

  • Sun, Jianwu
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.2
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    • pp.369-378
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    • 2001
  • In this paper, we obtain the following results: Let f be a transcendental entire function with log M(r,f)=$O(log r)^\beta (e^{log r}^\alpha)\; (0\leq\alpha<1,\beta>1$). Then every component of N(f) is bounded. This result generalizes the result of Baker.

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MEASURES OF COMPARATIVE GROWTH ANALYSIS OF COMPOSITE ENTIRE FUNCTIONS ON THE BASIS OF THEIR RELATIVE (p, q)-TH TYPE AND RELATIVE (p, q)-TH WEAK TYPE

  • Biswas, Tanmay
    • The Pure and Applied Mathematics
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    • v.26 no.1
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    • pp.13-33
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    • 2019
  • The main aim of this paper is to establish some comparative growth properties of composite entire functions on the basis of their relative (p, q)-th order, relative (p, q)-th lower order, relative (p, q)-th type, relative (p, q)-th weak type of entire function with respect to another entire function where p and q are any two positive integers.

RELATIVE LOGARITHMIC ORDER OF AN ENTIRE FUNCTION

  • Ghosh, Chinmay;Bandyopadhyay, Anirban;Mondal, Soumen
    • Korean Journal of Mathematics
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    • v.29 no.1
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    • pp.105-120
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    • 2021
  • In this paper, we extend some results related to the growth rates of entire functions by introducing the relative logarithmic order ����g(f) of a nonconstant entire function f with respect to another nonconstant entire function g. Next we investigate some theorems related the behavior of ����g(f). We also define the relative logarithmic proximate order of f with respect to g and give some theorems on it.

ON A GENERALIZATION OF THE P$\'{O}$LYA-WIMAN CONJECTURE

  • Kim, Young-One
    • Communications of the Korean Mathematical Society
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    • v.9 no.4
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    • pp.825-830
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    • 1994
  • This paper is concerned with the zeros of successive derivatives of real entire functions. In order to state our results, we introduce the following notations : An entire function which assumes only real values on the real axis is said to be a real entire function. Thus, if a complex number is a zero of a real entire function, then its conjugate is also a zero of the same function.

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A NOTE ON VALUE DISTRIBUTION OF COMPOSITE ENTIRE FUNCTIONS

  • Lahiri, Indrajit
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.1-6
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    • 2001
  • We discuss the value distribution of composite entire functions including those of infinite order and estimate the number of Q-points of such functions for an entire function Q or relatively slower growth.

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ON THE TRANSCENDENTAL ENTIRE SOLUTIONS OF A CLASS OF DIFFERENTIAL EQUATIONS

  • Lu, Weiran;Li, Qiuying;Yang, Chungchun
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.1281-1289
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    • 2014
  • In this paper, we consider the differential equation $$F^{\prime}-Q_1=Re^{\alpha}(F-Q_2)$$, where $Q_1$ and $Q_2$ are polynomials with $Q_1Q_2{\neq}0$, R is a rational function and ${\alpha}$ is an entire function. We consider solutions of the form $F=f^n$, where f is an entire function and $n{\geq}2$ is an integer, and we prove that if f is a transcendental entire function, then $\frac{Q_1}{Q_2}$ is a polynomial and $f^{\prime}=\frac{Q_1}{nQ_2}f$. This theorem improves some known results and answers an open question raised in [16].

AN ENTIRE FUNCTION SHARING A POLYNOMIAL WITH LINEAR DIFFERENTIAL POLYNOMIALS

  • Ghosh, Goutam Kumar
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.495-505
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    • 2018
  • The uniqueness problems on entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results on this topic have been obtained. In this paper, we study an entire function f(z) that shares a nonzero polynomial a(z) with $f^{(1)}(z)$, together with its linear differential polynomials of the form: $L=L(f)=a_1(z)f^{(1)}(z)+a_2(z)f^{(2)}(z)+{\cdots}+a_n(z)f^{(n)}(z)$, where the coefficients $a_k(z)(k=1,2,{\ldots},n)$ are rational functions and $a_n(z){\not{\equiv}}0$.