Multivariable Laurent Series Is it possible to Laurent Expand over two complex variables? for example 
$\frac{w+\tilde{w}}{(w\tilde{w})^{3}}$
where $w=i\sqrt{2}z+\hat{d}x+i\hat{e}y$ and $\tilde{w}=i\sqrt{2}z-\hat{d}x-i\hat{e}y$
Can someone point me in the right direction? i don't seem to be able to find much for more than 1 complex function..

It is possible, depending on the domain of the function. 
In your example, if you take a point on the smooth part of the pole divisor, you can find a product of annuli of small radii where the function is holomorphic. Then construct the Laurent series the same way as in one variable, by Cauchy's integral.
I'd refer to  Shabat's book, see page 35. It rather brief but may help. 
