Lagrange’s formula is a classical formula for constructing an interpolation polynomial. It allows us to obtain a unique polynomial of degree $n$ that passes through a given set of $(n+1)$ nodes $(x_k, y_k),{}_{k \in \left\{0, ..., n\right\}}$:

where:

• $x_i$ are the coordinates of the nodes,
• $y_i$ are the function values at these points,
• $l_i(x) = \prod_{j \ne i}{\frac{x-x_j}{x_i-x_j}}$ is the Lagrange basis polynomial for each point, which equals 1 when $x = x_i$ and 0 when $x = x_j$ for $j \neq i$.