Remarkable property of the periodic series. (Q1555993)
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scientific article; zbMATH DE number 2713866
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Remarkable property of the periodic series. |
scientific article; zbMATH DE number 2713866 |
Statements
Remarkable property of the periodic series. (English)
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1876
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Die aus \(n\) Gliedern bestehende Reihe \(\varSigma a_{k} \sin kx\) soll durch passende Wahl der Coefficienten \(a_{k}\) für alle Werthe des \(x\) zwischen 0 und \(\pi\) in möglichst nahe Uebereinstimmung mit den Werthen einer beliebigen Function \(F(x)\) gebracht werden. Man findet für \(a_{k}\) {\textit{unabhängig von}} \(n\) den Coefficienten der Fourier'schen Reihe \[ \frac{2}{\pi} \int_{0}^{\pi} F(x) \sin kx dx. \]
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Fourier coefficients
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trigonometric polynomials
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approximation
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