\[I_{-\nu}\left(x\right)-\mathbf{L}_{\nu}\left(x\right)=\frac{2(\tfrac{1}{2}x)^{%
\nu}}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{1}{2}\right)}\int_{0}^{\infty}(1+t^{2})%
^{\nu-\frac{1}{2}}\sin\left(xt\right)\,\mathrm{d}t,\]