On Picard's solution of \(\Delta u = k^2u\). (Q1466119)
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scientific article; zbMATH DE number 2606899
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Picard's solution of \(\Delta u = k^2u\). |
scientific article; zbMATH DE number 2606899 |
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On Picard's solution of \(\Delta u = k^2u\). (English)
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1920
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Die von Picard bei \(k = 1\) gegebene Lösung \(u =\int_{- \infty}^{-1} \frac {e^{zr}dz}{\sqrt {z^2-1}}(r = +\sqrt{x^2 +y^2})\) von \(\Delta u = k^2u\) wird für allgemeines \(k\) auf die Form \[ \int_0^\infty \text{exp} \left(-x^2 + \frac{a^2}{x^2}\right) \frac {dx}x\;(2a =k\sqrt{x^2 +y^2}) \] gebracht und ihr Verhalten für \(a \to 0\) und für \(a \to \infty\) untersucht.
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