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Update chebyshev.md
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mrhardman authored Jul 22, 2024
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Expand Up @@ -35,8 +35,7 @@ Assuming that $M = 2N$, with $N$ an integer, and $b_{k} = b_{M-k}$ for $k>0$, we
\begin{equation} f_j = b_{0} + b_{N}(-1)^j + \sum_{n=1}^{N-1}
b_{n}\left(\exp\left[i \frac{\pi n j}{N}\right]+\exp\left[-i \frac{\pi n j}{N}\right]\right).\end{equation}
```
Comparing this to the expression for $f(x_j)$ in the Chebyshev representation,
using the form of $T_n(x_j)$,
Comparing this to the expression for $f(x_j)$ in the Chebyshev representation,
```math
\begin{equation} f_j = a_{0} + a_{N}(-1)^j + \frac{1}{2}\sum_{n=1}^{N-1}
a_{n}\left(\exp\left[i \frac{\pi n j}{N}\right]+\exp\left[-i \frac{\pi n j}{N}\right]\right),\end{equation}
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