\[\left({\mathsf{i}^{(1)}_{n}}\left(z\right)\right)^{2}-\left({\mathsf{i}^{(2)}_%
{n}}\left(z\right)\right)^{2}=(-1)^{n+1}\sum_{k=0}^{n}(-1)^{k}\frac{s_{k}(n+%
\frac{1}{2})}{z^{2k+2}}.\]