\[\int_{-\infty}^{\infty}e^{ibt}\mathsf{j}_{n}\left(t\right)\,\mathrm{d}t=\begin%
{cases}\pi i^{n}P_{n}\left(b\right),&-1<b<1,\\
\frac{1}{2}\pi(\pm\mathrm{i})^{n},&b=\pm 1,\\
0,&\pm b>1,\end{cases}\]