A definite integral for Legendre functions. (Q2596456)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A definite integral for Legendre functions. |
scientific article |
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A definite integral for Legendre functions. (English)
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1938
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Verf. beweist: \[ P_n\left(\frac1{xy}\right)=\frac1{2\pi} \int\limits_0^{2\pi} \left(1 + i\frac{1+xy}{y^2} e^{-i\gamma}\right) ^{\frac n2} \left(1-i\frac{1-xy}{x^2} e^{i\gamma}\right) ^{-\frac{n+1}2}\, d\gamma \] für die Kugelfunktionen und entsprechende Integraldarstellungen für zugeordnete Kugelfunktionen und für Jacobische Polynome.
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