From 99524349daae12733b5d48fb220c1d5b551219c6 Mon Sep 17 00:00:00 2001 From: siveshs Date: Fri, 2 Jul 2010 03:24:56 +0000 Subject: still testing --- Fourier Series.page | 8 ++++---- 1 file 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? -- cgit v1.2.3