still testing

1 files changed, 4 insertions, 4 deletions

diff --git a/Fourier Series.page b/Fourier Series.page
index c90f37e..ad3c6d8 100644
--- a/Fourier Series.page
+++ b/Fourier Series.page
@@ -7,10 +7,10 @@ To show that Fourier series is plausible, let us consider some arbitrary trignom
  $1.  \cos(2x) = 1 - 2 \sin^2(x)$
 
 $$\begin{array}{ccl} 
-e^{iy}  =  1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\
-  =  1+iy-\frac{y^{2}}{2!}-i\frac{y^{3}}{3!}+\frac{y^{4}}{4!}+i\frac{y^{5}}{5!}+\cdots\\
-  =  (1-\frac{y^{2}}{2!}+\frac{y^{4}}{4!}+\cdots)+i(y-\frac{y^{3}}{3!}+\frac{y^{5}}{5!}-\cdots)\\
-  =  \cos y+i\sin y\end{array}$$
+e^{iy} & =  1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\
+ & =  1+iy-\frac{y^{2}}{2!}-i\frac{y^{3}}{3!}+\frac{y^{4}}{4!}+i\frac{y^{5}}{5!}+\cdots\\
+ & =  (1-\frac{y^{2}}{2!}+\frac{y^{4}}{4!}+\cdots)+i(y-\frac{y^{3}}{3!}+\frac{y^{5}}{5!}-\cdots)\\
+ & =  \cos y+i\sin y\end{array}$$
   
 ##What is the Fourier series actually?</b>