Formula:4667

Digital Library of Mathematical Functions ID 11.5.E3

${\displaystyle{\displaystyle\mathbf{K}_{0}\left(z\right)=\frac{2}{\pi}\int_{0}^{\infty}e^{-z\sinh t}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle\Re z>0}}$

Symbols List

• ${\displaystyle{\displaystyle\mathbf{K}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Struve function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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