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| -rw-r--r-- | Fourier Series.page | 6 |
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diff --git a/Fourier Series.page b/Fourier Series.page index b603912..c90f37e 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -8,9 +8,9 @@ To show that Fourier series is plausible, let us consider some arbitrary trignom $$\begin{array}{ccl} e^{iy} = 1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\ - & = & 1+iy-\frac{y^{2}}{2!}-i\frac{y^{3}}{3!}+\frac{y^{4}}{4!}+i\frac{y^{5}}{5!}+\cdots\\ - & = & (1-\frac{y^{2}}{2!}+\frac{y^{4}}{4!}+\cdots)+i(y-\frac{y^{3}}{3!}+\frac{y^{5}}{5!}-\cdots)\\ - & = & \cos y+i\sin y\end{array}$$ + = 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> |