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| -rw-r--r-- | Fourier Series.page | 5 |
1 files changed, 2 insertions, 3 deletions
diff --git a/Fourier Series.page b/Fourier Series.page index 6159544..204d0f4 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -5,9 +5,8 @@ We first begin with a few basic identities on the size of sets. Show that the se ##Why Fourier series is plausible?</b> To show that Fourier series is plausible, let us consider some arbitrary trignometric functions and see if it is possible to express them as the sum of sines and cosines: -$$ -\sin^2(x) = ?\\ -\begin{array}{ccl} +$$\sin^2(x) = ?$$ +$$\begin{array}{ccl} & = & 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}$$ |