A part of a letter to M. Liouville. (Q1558762)
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scientific article; zbMATH DE number 2716693
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A part of a letter to M. Liouville. |
scientific article; zbMATH DE number 2716693 |
Statements
A part of a letter to M. Liouville. (English)
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1874
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Ohne Beweis mitgetheilt wird die Transformation \[ \int_0^\pi\frac{\partial x[f(e^{ix})+ f(e^{-ix})]} {\sqrt{1- 2\alpha\cos x+\alpha^2}}=2 \int_0^\pi\frac{f(a\sin^2x)\partial x} {\sqrt{1-a^2\sin^2x}}, \] wo \(a\) der absolute Werth von \(\alpha\) und \(<1\), \(f\) eine durch die Maclaurin'sche Reihe darstellbare Function ist.
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Explicit integration
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