 Lagrange cardinal polynomial (source code)

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= Lagrange cardinal polynomial
{c}
{title2=$\ell_i$}

= Lagrange basis polynomial
{c}
{synonym}

For distinct <interpolation nodes> $x_0,\ldots,x_n$, the polynomial $\ell_i(x)=\prod_{j\ne i}(x-x_j)/(x_i-x_j)$ has $\ell_i(x_j)=\delta_{ij}$. These cardinal polynomials form a <basis> of the <polynomials> of degree at most $n$, and give $p(x)=\sum_i p(x_i)\ell_i(x)$.

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