update

pages/Math416/Math416_L15.md

@@ -34,7 +34,7 @@ Proof:
 
 Let $z_0\in G$. There exists a neighborhood $\overline{B_r(z_0)}\subset G$ of $z_0$ such that $\left(f_n\right)_{n\in\mathbb{N}}$ converges uniformly on $\overline{B_r(z_0)}$.
 
-Let $C_r=partial B_r(z_0)$.
+Let $C_r=\partial B_r(z_0)$.
 
 By Cauchy integral formula, we have
 
@@ -42,7 +42,7 @@ $$
 f_n(z_0) = \frac{1}{2\pi i}\int_{C_r}\frac{f_n(\zeta)}{\zeta-z_0}d\zeta
 $$
 
-$\forall z\in B_r(z_0)$, we have $\frac{f_n(w)}{w-\zeta}$ converges uniformly on $C_r$.
+$\forall z\in B_r(z_0)$, we have $\frac{f(w)}{w-\zeta}$ converges uniformly on $C_r$.
 
 So $\lim_{n\to\infty}f_n(z_0) = f(z_0) = \frac{1}{2\pi i}\int_{C_r}\frac{f(w)}{w-z_0}dw$