Asymptotic properties of functions holomorphic on the unit disk (Q2754808)
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scientific article; zbMATH DE number 1668432
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic properties of functions holomorphic on the unit disk |
scientific article; zbMATH DE number 1668432 |
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4 November 2001
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power series
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order of power growth
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type of power growth
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Asymptotic properties of functions holomorphic on the unit disk (English)
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The author considers power series \(F(z)=\sum_{n=1}^\infty A_nz^{\lambda_n}\), where \(\lambda_n\) are natural numbers and \(\varlimsup\limits_{n\to \infty}\frac{\log \log n}{\log \log \lambda_n}<1\). Assuming that the convergence radius is equal to 1, the author finds explicit formulas for the order and type of power growth of \(F(z)\) as \(|z|\to 1\).
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0.7936397790908813
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