Formula:4332

Digital Library of Mathematical Functions ID 10.43.E21

${\displaystyle{\displaystyle\int_{0}^{\infty}\sin\left(at\right)K_{0}\left(t\right)\mathrm{d}t=\frac{\operatorname{arcsinh}a}{(1+a^{2})^{\frac{1}{2}}},}}$

Constraint(s)

${\displaystyle{\displaystyle|\Im a|<1}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\Im}}$: imaginary part
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
 

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