\begin{align}
    & d_{NIG_{d}}\left(x; \alpha,\beta,\delta,\mu,\Delta \right)= \sqrt{\frac{2}{\pi}} \frac{\delta \alpha^{\frac{d+1}{2}}}{\left(2 \pi 
    \right)^{\frac{d}{2}}}  e^{\delta\sqrt{\alpha^{2}-\beta' \Delta \beta}}  \left(  \left(x-\mu\right)'\Delta^{-1}\left(x-\mu\right)+
    \delta^{2}\right)^{-\frac{d+1}{4}} \cdot \nonumber\\
   & \cdot K_{\frac{d+1}{2}}\left( \alpha \sqrt{ \left(x-\mu\right)'\Delta^{-1}\left(x-\mu\right)+\delta^{2} } \right)e^{\beta' \left( x-
   \mu\right)}.
\end{align}
