\[\mathbf{L}_{\nu}\left(z\right)=-ie^{-\frac{1}{2}\pi i\nu}\mathbf{H}_{\nu}\left%
(iz\right)=(\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac{(\tfrac{1}{2}z)^{2n%
}}{\Gamma\left(n+\tfrac{3}{2}\right)\Gamma\left(n+\nu+\tfrac{3}{2}\right)}.\]