DLMF:10.22.E55

MaRDI QIDQ4126

• Label: DLMF:10.22.E55

Digital Library of Mathematical Functions ID 10.22.E55

${\displaystyle{\displaystyle\int_{0}^{\infty}t^{-1}J_{\nu+2\ell+1}\left(t\right)J_{\nu+2m+1}\left(t\right)\mathrm{d}t=\frac{\delta_{\ell,m}}{2(2\ell+\nu+1)},}}$

Constraint(s)

${\displaystyle{\displaystyle\nu+\ell+m>-1}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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