Formula:4321

Digital Library of Mathematical Functions ID 10.43.E10

${\displaystyle{\displaystyle\int_{x}^{\infty}e^{t}t^{-\nu}K_{\nu}\left(t\right)\mathrm{d}t=\frac{e^{x}x^{-\nu+1}}{2\nu-1}(K_{\nu}\left(x\right)+K_{\nu-1}\left(x\right)),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re\nu>\tfrac{1}{2}}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

Resources that cite this formula

No records found.