DLMF:10.43.E27

MaRDI QIDQ4338

• Label: DLMF:10.43.E27

Digital Library of Mathematical Functions ID 10.43.E27

${\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu+\nu+1}K_{\mu}\left(at\right)J_{\nu}\left(bt\right)\mathrm{d}t=\frac{(2a)^{\mu}(2b)^{\nu}\Gamma\left(\mu+\nu+1\right)}{(a^{2}+b^{2})^{\mu+\nu+1}},}}$

Constraint(s)

${\displaystyle{\displaystyle\Re(\nu+1)>|\Re\mu|,\Re a>|\Im b|}}$

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
• ${\displaystyle{\displaystyle\Im}}$: imaginary part
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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