Meromorphic function of infinite order with maximum deficiency sum (Q1769798)
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scientific article; zbMATH DE number 2149308
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Meromorphic function of infinite order with maximum deficiency sum |
scientific article; zbMATH DE number 2149308 |
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Meromorphic function of infinite order with maximum deficiency sum (English)
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30 March 2005
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The author proves that \[ \limsup_{r\to\infty}\frac{N(r,1/f^{(k)})+N(r,f^{(k)})}{T(r,f^{(k)})}= \frac{2k[1-\delta(\infty,f)]}{1+k-k\delta(\infty,f)}, \] for each integer \(k\geq 1\) and each transcendental meromorphic function \(f\) satisfying \(\sum_{a\not=\infty}\delta(a,f)+\delta(\infty,f)=2\). This result improves the results of S. K. Singh and V.~N.~Kulkarni, and M. L. Fang.
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meromorphic function
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deficiency
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maximum deficiency sum
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0.9635703
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0.92219067
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0.9172807
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