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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Xiao-Guang Qi, Lian-Zhong Yang (2011)
Annales Polonici Mathematici
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We give some growth properties for solutions of linear complex differential equations which are closely related to the Brück Conjecture. We also prove that the Brück Conjecture holds when certain proximity functions are relatively small.
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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S. K. Singh (1976)
Matematički Vesnik
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Francois Gramain (1981)
Inventiones mathematicae
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Hiroyuki Yoshida (1973)
Inventiones mathematicae
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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).
L. S. O. Liverpool, Umaru Umar (1982)
Publications de l'Institut Mathématique
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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.
H.G. Diamond, C. Pomerance, L. Rubel (1981)
Mathematische Zeitschrift
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A.P. OGG (1969/70)
Inventiones mathematicae
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Henryk Hecht, Winfried Schmid (1976)
Inventiones mathematicae
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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.