Mythical Bears

Mathematics Bear

This page contains formulas used by mathematically inclined bears.  Very few of these bears are found in the wild.  It is believed that a small family live near Meyrin, Switzerland.

Albert Einstein’s famous formula E=mc^2 can be used ….

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At first, we sample f(x) in the N (Nis odd) equidistant points around x^*:
   f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
where h is some step.
Then we interpolate points \{(x_k,f_k)\} by polynomial 
\begin{equation} \label{eq:poly}
Its coefficients \{a_j\} are found as a solution of system of linear equations:
\begin{equation} \label{eq:sys}
   \left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
Here are references to existing equations: (ref{eq:poly}), (ref{eq:sys}).
Here is reference to non-existing equation (ref{eq:unknown}).



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