On a power series which is uniformly but not absolutely convergent on the whole circle of convergence. (Q1470961)
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scientific article; zbMATH DE number 2611219
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a power series which is uniformly but not absolutely convergent on the whole circle of convergence. |
scientific article; zbMATH DE number 2611219 |
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On a power series which is uniformly but not absolutely convergent on the whole circle of convergence. (English)
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1918
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Aus der unendlichen Reihe \[ P(z)=\sum_{n=1}^\infty\frac{(-1)^{n-1}}{2^n\cdot n}(z^{2^{n- 1}}+\cdots+z^{2^n-1}) \] erhält man durch Weglassen der Klammern die Reihe \[ Q(z)=\frac z2-\frac{z^2}{8}- \frac{z^3}{8}+\frac{z^4}{24}+\frac{z^5}{24}+\frac{z^6}{24}+\frac{z ^7}{24}-\cdots, \] welche auf dem Kreise \(| z| =1\) gleichmäßig, aber nicht absolut konvergiert.
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