\[\int_{0}^{\infty}\cos\left(2xt\right){\mathbf{M}}\left(a,b,-t^{2}\right)\,%
\mathrm{d}t=\frac{\sqrt{\pi}}{2\Gamma\left(a\right)}x^{2a-1}e^{-x^{2}}U\left(b%
-\tfrac{1}{2},a+\tfrac{1}{2},x^{2}\right),\]