A note on the value distribution of \(f^1(f^{(k)})^n\) (Q330669)
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scientific article; zbMATH DE number 6643501
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the value distribution of \(f^1(f^{(k)})^n\) |
scientific article; zbMATH DE number 6643501 |
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A note on the value distribution of \(f^1(f^{(k)})^n\) (English)
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26 October 2016
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meromorphic functions
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value distribution
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The value distribution of \(f^{l}(f^{(k)})^{n}\) is discussed and the following result is proved: Let \(f\) be a transcendental meromorphic function in \(\mathbb{C}\), let \(l>1\), \(n >1\), \(k >1\) be integers, and let \(a\) be a nonzero constant. Then NEWLINE\[NEWLINE(l - 1)T(r, f) \leq N\big(r, 0; f^{l}(f^{(k)})^{n} - a\big) + S^{*}(r, f),NEWLINE\]NEWLINE where \(S^{*}(r, f) = o\{T(r, f)\}\) as \(r \to \infty\), possibly outside a set of logarithmic density zero.
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