\displaystyle{f(z) = sin(z)\cdot sin(\frac{1}{z}) = (\frac{z}{1!} - \frac{z^3}{3!} + \frac{z^5}{5!} - \ldots )\cdot (\frac{1}{z\cdot 1!} - \frac{1}{z^3\cdot 3!} + \frac{1}{z^5\cdot 5!} - \ldots )}