The Ritt order of the derivative of an entire function
Q. I. Rahman (1965)
Annales Polonici Mathematici
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Q. I. Rahman (1965)
Annales Polonici Mathematici
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P. K. Kamthan, P. K. Jain (1969)
Annales Polonici Mathematici
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Domar, Yngve (1997)
Annales Academiae Scientiarum Fennicae. Mathematica
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S. K. Vaish, H. S. Kasana (1982)
Publications de l'Institut Mathématique
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Bogusława Karpińska (2003)
Fundamenta Mathematicae
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We prove that for some families of entire functions whose Julia set is the complement of the basin of attraction every branch of a tree of preimages starting from this basin is convergent.
Feng Lü, Junfeng Xu (2012)
Annales Polonici Mathematici
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Applying the normal family theory and the theory of complex differential equations, we obtain a uniqueness theorem for entire functions that share a function with their first and second derivative, which generalizes several related results of G. Jank, E. Mues & L. Volkmann (1986), C. M. Chang & M. L. Fang (2002) and I. Lahiri & G. K. Ghosh (2009).
Indrajit Lahiri, Gautam Kumar Ghosh (2009)
Annales Polonici Mathematici
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We study the uniqueness of entire functions which share a value or a function with their first and second derivatives.
Małgorzata Downarowicz, Adam Janik (1985)
Annales Polonici Mathematici
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A. E. Eremenko (1989)
Banach Center Publications
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S. K. Singh (1976)
Matematički Vesnik
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Sheng Li, Zongsheng Gao, Jilong Zhang (2012)
Annales Polonici Mathematici
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We investigate the uniqueness of entire functions sharing values or small functions with their derivatives. One of our results gives a necessary condition on the Nevanlinna deficiency of the entire function f sharing one nonzero finite value CM with its derivative f'. Some applications of this result are provided. Finally, we prove some further results on small function sharing.
Fricke, G.H., Roy, Ranjan, Shah, S.M. (1981)
International Journal of Mathematics and Mathematical Sciences
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S. K. Bajpai, S. K. Singh-Gautam, S. S. Bajpai (1980)
Annales Polonici Mathematici
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L. S. O. Liverpool, Umaru Umar (1982)
Publications de l'Institut Mathématique
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Irvine Noel Baker (1962)
Mathematische Zeitschrift
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Stefan Halvarsson (1996)
Annales Polonici Mathematici
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We study the growth of parameter-dependent entire functions. We are mainly interested in the case where the functions depend holomorphically on the parameter.