Formula:4122

Digital Library of Mathematical Functions ID 10.22.E51

${\displaystyle{\displaystyle\int_{0}^{\infty}J_{\nu}\left(bt\right)\exp\left(-p^{2}t^{2}\right)t^{\nu+1}\mathrm{d}t=\frac{b^{\nu}}{(2p^{2})^{\nu+1}}\exp\left(-\frac{b^{2}}{4p^{2}}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re\nu>-1}}$
${\displaystyle{\displaystyle\Re(p^{2})>0}}$

Symbols List

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

Resources that cite this formula

No records found.