From 4d5a5663e5983d2846f980d6cbb5ca2ae54a8706 Mon Sep 17 00:00:00 2001 From: siveshs Date: Fri, 2 Jul 2010 03:24:10 +0000 Subject: still testing --- Fourier Series.page | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Fourier Series.page b/Fourier Series.page index a050d70..b603912 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -7,7 +7,7 @@ To show that Fourier series is plausible, let us consider some arbitrary trignom $1. \cos(2x) = 1 - 2 \sin^2(x)$ $$\begin{array}{ccl} -e^{iy} & = & 1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\ +e^{iy} = 1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\ & = & 1+iy-\frac{y^{2}}{2!}-i\frac{y^{3}}{3!}+\frac{y^{4}}{4!}+i\frac{y^{5}}{5!}+\cdots\\ & = & (1-\frac{y^{2}}{2!}+\frac{y^{4}}{4!}+\cdots)+i(y-\frac{y^{3}}{3!}+\frac{y^{5}}{5!}-\cdots)\\ & = & \cos y+i\sin y\end{array}$$ -- cgit v1.2.3