\[\mathbf{K}_{n+\frac{1}{2}}\left(z\right)=\left(\frac{2}{\pi z}\right)^{\frac{1%
}{2}}\sum_{m=0}^{n}\frac{(2m)!\,2^{-2m}}{m!\,(n-m)!}\,(\tfrac{1}{2}z)^{n-2m},\]