How Can We Calculate Coefficients in Multivariable Laurent Series?

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zetafunction
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can we define a multivariable power series (laurent series)

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

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

how could i calculate the coefficients ?? [tex]a_{i,j,k,l}[/tex] ?
 
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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.