latex

1 files changed, 1 insertions, 1 deletions

diff --git a/ClassJuly5.page b/ClassJuly5.page
index d740cf7..8f59ebf 100644
--- a/ClassJuly5.page
+++ b/ClassJuly5.page
@@ -27,7 +27,7 @@ $$c_{-1} = \frac{1}{2 \pi i}\int_{\gamma_r} f(z) dz$$
 where $\gamma$ is a small circle of radius $r$ that takes one counterclockwise turn around the origin.  Taking the limit as $r \to 0$, we find ourselves integrating over a circle of radius $0$:
 $$ c_{-1} = \frac{1}{2 \pi i} \lim_{r \to 0} \int_{\gamma_r} f(z) dz = \frac{1}{2 \pi i} \int_{\gamma_0} f(z) dz = \frac{1}{2 \pi i} \int_0^{2\pi} f(0) \frac{d\gamma_0}{dt} dt$$
 But $\gamma_0(t) = 0$, hence $\frac{d \gamma_0}{dt} = 0$.  We conclude that
-$$c_{-1} = \frac{1}{2 \pi i} \int_0^{2\pi} 0 dt  = 0 $.
+$$c_{-1} = \frac{1}{2 \pi i} \int_0^{2\pi} 0 dt  = 0 $$
 
 Now let's prove that $c_{-2}$ has to be zero.  Consider the function 
 $$ g(z) = z f(z) = \cdots \frac{c_{-3}}{z^2} + \frac{c_{-2}}{z} + c_{-1} + c_0 z + c_1 z^2 + \cdots $$