\[\mathbf{K}_{\nu}\left(z\right)=\frac{2(\tfrac{1}{2}z)^{\nu}}{\sqrt{\pi}\Gamma%
\left(\nu+\tfrac{1}{2}\right)}\int_{0}^{\infty}e^{-zt}(1+t^{2})^{\nu-\frac{1}{%
2}}\,\mathrm{d}t,\]