@Matt Groff: I'm a little bit curious, at least, though with different variables I'm not sure that it qualifies as a 'Hadamard Product' per se. Maybe an examle would be in order: to use the classic example, what closed-form does your formula provide for the Hadamard product of $e^{x/2}$ and $e^{-y/2}$? –  Steven Stadnicki Aug 12 '11 at 21:51
@Steven Stadnicki:$\frac{1}{3}(\frac{1}{2}(e^{\frac{x}{2}-\frac{y}{2}}+e^{-\frac{x}{2}+\‌​frac{y}{2}})$+$1/2(e^{1/2e^{2i\pi /3}x-1/2e^{-2i\pi /3}y}$+$e^{-1/2e^{2i\pi /3}x+1/2e^{-2i\pi /3}y})$+$1/2(e^{1/2e^{-2i\pi /3}x-1/2e^{2i\pi /3}y}$+$e^{-1/2e^{-2i\pi /3}x+1/2e^{2i\pi /3}y}))$. Sorry for the slow reply. I think this formula is correct, if it displays ok... –  Matt Groff Aug 13 '11 at 1:28