Benedict Irwin edited Random.tex  over 9 years ago

Commit id: 7587490b04ed2384e2b2a55238a02b9ce108f8df

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\sum_{i=-\infty}^{\infty} f(x_i)\prod_{j=-\infty}^\infty\frac{x-x_j}{x_i-x_j} = cos(x)  \end{equation}  For $f(x)=x$, $x_i=(-1)^i\pi$ $f(x_i)=(-1)^i$, $x_i=i\pi$  ?  We then have \begin{equation}  \sum_{i=-\infty}^{\infty} (-1)^i\pi\prod_{j=-\infty}^\infty\frac{x-(-1)^j\pi}{(-1)^i\pi-(-1)^j\pi} (-1)^i\prod_{j=-\infty}^\infty\frac{x-j\pi}{i\pi-j\pi}  = cos(x) \end{equation}