Two entire functions sharing one small function CM and two other small functions IM (Q5955578)
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scientific article; zbMATH DE number 1705564
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two entire functions sharing one small function CM and two other small functions IM |
scientific article; zbMATH DE number 1705564 |
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Two entire functions sharing one small function CM and two other small functions IM (English)
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22 March 2003
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entire function
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value distribution
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small function
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sharing value
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0.91639745
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0.9091695
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0.9029509
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0.89708924
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0.8914037
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0.8898179
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The author proves the following result: Let \(f\) and \(g\) be two nonconstant entire functions. Let \(a_1\), \(a_2\) and \(a_3\) be three distinct small meromorphic functions with respect to \(f\) and \(g\). If \(f\) and \(g\) share \(a_1\), \(a_2\) IM and share \(a_3\) CM, then NEWLINE\[NEWLINEf=\frac{\alpha_1 g+ \beta_1}{\alpha_2 g +\beta_2},NEWLINE\]NEWLINE where \(\alpha_i\), \(\beta_i\), \(i=1,2\), are small meromorphic functions with respect to \(f\) and \(g\). Here CM (resp., IM) is the abbreviation of counting multiplicity (resp., ignoring multiplicity). A more general result was obtained by \textit{P. Li} [J. Math. Anal. Appl. 263, 316-326 (2001; Zbl 1007.30020)].
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