Formula:4329

Digital Library of Mathematical Functions ID 10.43.E18

${\displaystyle{\displaystyle\int_{0}^{\infty}K_{\nu}\left(t\right)\mathrm{d}t=\tfrac{1}{2}\pi\sec\left(\tfrac{1}{2}\pi\nu\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|\Re\nu|<1}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: 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
• ${\displaystyle{\displaystyle\sec\NVar{z}}}$: secant function
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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