DLMF:10.32.E6

MaRDI QIDQ4223

• Label: DLMF:10.32.E6

Digital Library of Mathematical Functions ID 10.32.E6

${\displaystyle{\displaystyle K_{0}\left(x\right)=\int_{0}^{\infty}\cos\left(x\sinh t\right)\mathrm{d}t=\int_{0}^{\infty}\frac{\cos\left(xt\right)}{\sqrt{t^{2}+1}}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle x>0}}$

Symbols List

• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the second kind
• ${\displaystyle{\displaystyle x}}$: real variable
 

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