\({\rm{f}}\left( {\rm{z}} \right) = \frac{{{\rm{sinz}}}}{{{{\rm{z}}^2}}}\)
Expanding the sin term, we can write:
\(f(z) = \frac{1}{{{{\rm{z}}^2}}}\left[ {{\rm{z}} - \frac{{{{\rm{z}}^3}}}{{3!}} + \frac{{{{\rm{z}}^5}}}{{5!}} - \frac{{{{\rm{z}}^7}}}{{7!}} + \ldots } \right]\)
\(f(z)= \frac{1}{{\rm{z}}} - \frac{{\rm{z}}}{{3!}} + \frac{{{{\rm{z}}^3}}}{{5!}} - \ldots \)
Reside at z = 0 is the coefficient of \(\left( {\frac{1}{{\rm{z}}}} \right)\) in the expansion of f(z) i.e.
Residue R = 1
