\[\mathscr{F}_{\mkern-2.0mus}\left(f\right)\left(x\right)=\mathscr{F}_{\mkern-2.%
0mus}\mskip-1.0muf\mskip 3.0mu\left(x\right)=\sqrt{\frac{2}{\pi}}\int^{\infty}%
_{0}f(t)\sin\left(xt\right)\,\mathrm{d}t.\]