# Multivariable Laurent Series

1. Apr 7, 2010

### zetafunction

can we define a multivariable power series (laurent series)

$$\sum_{i,j,k,l,.....=-\infty}^{\infty}a_{i,j,k,l,......}(X-a)^{i}(Y-b)^{j}(Z-c)^{k}(W-k)^{l}....$$

indices i,j k and l run over ALL the integers positive and negatives

how could i calculate the coefficients ?? $$a_{i,j,k,l}$$ ?????

2. Apr 7, 2010

### g_edgar

Can you already do simpler cases? For example, only nonnegative exponents? Or just two variables? If not, work on those before you tackle this one.