Hankel transforms. (Q5908865)
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scientific article; zbMATH DE number 2598371
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hankel transforms. |
scientific article; zbMATH DE number 2598371 |
Statements
Hankel transforms. (English)
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1923
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Für \(a \to\infty\) konvergiert \(F_a(x) \equiv {\displaystyle\int_0^a} (ux)^{\frac12} J_\nu (ux) f(u)\, du\) im Mittel nach \[ F(x) = x^{-\nu-\frac12}\frac{d}{dx} \biggl\{ x^{\nu+1} \int_0^\infty u^{-\frac12} J_{\nu+1}(ux)f(u)\,du\biggr\}. \] Es heißt dann \(F(x)\) die Hankelsche Transformierte von \(f (x)\). Die Hankelsche Transformierte von \(F (x)\) gibt fast überall \(f (x)\). (IV 7.)
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