A note on the singular part of the Fourier-Bessel integral. (Q2594510)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A note on the singular part of the Fourier-Bessel integral. |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the singular part of the Fourier-Bessel integral. |
scientific article |
Statements
A note on the singular part of the Fourier-Bessel integral. (English)
0 references
1939
0 references
Unter Benutzung von Stieltjes-Integralen wird ein neuer Beweis des Satzes gegeben: Ist \(F (t)\) im Intervall \(0 <\alpha \leqq x\leqq \beta <\infty\) von beschränkter Variation, so ist für \(\nu > - 1\): \[ \int\limits_0^\infty J_\nu(ux) udu \int\limits_\alpha^\beta F (t) J_\nu (ut) t^{\nu+1} dt = \tfrac12x^\nu (F(x + 0) + F (x - 0)). \]
0 references
