The \textit{Lommel-Weber} \(\Omega\) function and its application to the Problem of electric waves on a thin anchor ring. (Q1471084)
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scientific article; zbMATH DE number 2611358
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \textit{Lommel-Weber} \(\Omega\) function and its application to the Problem of electric waves on a thin anchor ring. |
scientific article; zbMATH DE number 2611358 |
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The \textit{Lommel-Weber} \(\Omega\) function and its application to the Problem of electric waves on a thin anchor ring. (English)
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1918
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Es werden für die Funktion \[ \Omega_n(x)=\frac 1\pi\int_0^\pi\sin(x\sin\varphi- n\varphi)d\varphi, \] die in naher Beziehung steht zur \textit{Bessel}schen Funktion \(J_n(x)\), Reihenentwicklungen und Rekursionsformeln gegeben mit Hilfe der \textit{Neumann}schen Funktionen \(Y_n(x)\) und der \textit{Schläfli}schen Polynome \(S_n(x)\). Die Funktionen \(\Omega_n(x)\) spielen u. a. eine Rolle in der Theorie der Interferenz und der Diffraktion.
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