# Is there a mistake in my book for the coefficients of Laurent series?

I am reading Complex Variables and Application by James Brown and Ruel Churchill and there something that doesn't seem right with the following:

If I set $b=1$ I get $$b_{1}=\frac{1}{2\pi i}\int_{C}\frac{f(z)}{(z-z_{0})^{-1+1}}\, dz=\frac{1}{2\pi i}\int_{C}\, f(z)\, dz$$

But from the part in the book that talks about residues and by the definition of Laurent series it seems that $$b_{1}=\frac{1}{2\pi i}\int_{C}\frac{f(z)}{z-z_{0}}\, dz$$

Is there a mistake in the formula for the coefficients $b_{n}$ in the book ? (are the $a_{n}$ OK ?)

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The book is right (wow!). You might want to explain more precisely why you think $b_1$ is the integral you write. –  Did Mar 20 '13 at 8:19