A probabilistic proof of the series representation of the Macdonald function with applications (Q1392694)
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scientific article; zbMATH DE number 1180636
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A probabilistic proof of the series representation of the Macdonald function with applications |
scientific article; zbMATH DE number 1180636 |
Statements
A probabilistic proof of the series representation of the Macdonald function with applications (English)
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8 March 1999
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The authors use probabilistic methods to expand \(K_{\alpha}(2z\sqrt{1-t})/(1-t)^{\alpha/2}\) as a power series in \(t\), where \[ K_{\alpha}(z) = \int_0^{\infty} \exp(-z \cosh t)\cosh(\alpha t) dt. \]
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