For $\mathrm{f}\left(\mathrm{z}\right)=\frac{\sin \left(\mathrm{z}\right)}{{\mathrm{z}}^2}$ the residue of the pole at z = 0 is __________

In the range: 1 - 1

$\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{sinz}}{{\mathrm{z}}^2}$

Expanding the sin term, we can write:

$f(z)=\frac{1}{{\mathrm{z}}^2}\left[\mathrm{z}-\frac{{\mathrm{z}}^3}{3!}+\frac{{\mathrm{z}}^5}{5!}-\frac{{\mathrm{z}}^7}{7!}+\dots \right]$

$f(z)=\frac{1}{\mathrm{z}}-\frac{\mathrm{z}}{3!}+\frac{{\mathrm{z}}^3}{5!}-\dots$

Reside at z = 0 is the coefficient of $\left(\frac{1}{\mathrm{z}}\right)$ in the expansion of f(z) i.e.

Residue R = 1