DLMF:10.22.E62

MaRDI QIDQ4133

• Label: DLMF:10.22.E62

Digital Library of Mathematical Functions ID 10.22.E62

${\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu-\nu+1}J_{\mu}\left(at\right)J_{\nu}\left(bt\right)\mathrm{d}t=\begin{cases}0,&0<b<a,\\ \dfrac{2^{\mu-\nu+1}a^{\mu}(b^{2}-a^{2})^{\nu-\mu-1}}{b^{\nu}\Gamma\left(\nu-\mu\right)},&0<a\leq b.\end{cases}}}$

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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