Latex 2

My First Web Page

My First Paragraph

At first, we sample f(x) in the N (N is 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 Its coefficients \{a_j\} are found as a solution of system of linear equations:

(1)   \begin{equation*} \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: (2), (1). Here is reference to non-existing equation (\href{https://www.example.com}). Here is reference to non-existing equation \url{http://www.overleaf.com} This is my link: 2) \href{http://www.latex-tutorial.com}{LaTeX-Tutorial}.

(2)   \begin{equation*} P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j} \end{equation*}

Rendered by QuickLaTeX.com

//——————————————————————————-