DLMF:10.43.E19

MaRDI QIDQ4330

• Label: DLMF:10.43.E19

Digital Library of Mathematical Functions ID 10.43.E19

${\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu-1}K_{\nu}\left(t\right)\mathrm{d}t=2^{\mu-2}\Gamma\left(\tfrac{1}{2}\mu-\tfrac{1}{2}\nu\right)\Gamma\left(\tfrac{1}{2}\mu+\tfrac{1}{2}\nu\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|\Re\nu|<\Re\mu}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: 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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