Inequalities for the logarithmic derivatives of a polynomial. (Q5921959)
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scientific article; zbMATH DE number 2506364
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inequalities for the logarithmic derivatives of a polynomial. |
scientific article; zbMATH DE number 2506364 |
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Inequalities for the logarithmic derivatives of a polynomial. (English)
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1940
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Es gilt z. B. \[ \left|{\sum\limits_{k=1}^{n}}(a_k-z)^{-m}\right| < \frac{n^{m\alpha}}{H^m}{\sum\limits_{p=1}^{n}}p^{-m\alpha}, \] falls \(z\) außerhalb von höchstens \(n\) Kreisen liegt, deren Radien \(h_k\) die Ungleichung \(\sum h_k^{\tfrac1\alpha}\leqq(2H)^{\tfrac1\alpha}\) erfüllen, \(H> 0\), \(\alpha > 0\).
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