Show that $\Phi$($\phi$) = $e$$^{im_l}$$^\phi$ = $\Phi$($\phi$ + 2$\pi$) (that is, show that $\Phi$ ($\phi$) is periodic with period 2$\pi$) if and only if m$_l$ is restricted to the values 0, $\pm$1, $\pm$2,.... ($Hint$: Euler's formula states that $e$$^i$$^\phi$ = cos $\phi$ + $i$ sin $\phi$.)