\[\mathbf{L}_{\frac{3}{2}}\left(z\right)=-\left(\frac{z}{2\pi}\right)^{\frac{1}{%
2}}\left(1-\frac{2}{z^{2}}\right)+\left(\frac{2}{\pi z}\right)^{\frac{1}{2}}%
\left(\sinh z-\frac{\cosh z}{z}\right),\]