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 can be used ….

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At first, we sample in the (is odd) equidistant points around :
\[
   f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\]
where is some step.
Then we interpolate points by polynomial 
\begin{equation} \label{eq:poly}
   P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}
\end{equation}
Its coefficients 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}
\end{equation}
Here are references to existing equations: (), ().
Here is reference to non-existing equation ().