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Let $n\in\mathbb{N}^*,A=(a_1,\dots,a_n)\in\mathbb{K}[X]^n$ all different numbers and $B=(b_1,...,b_n)\in\mathbb{K}[X]^n$ all different numbers.

Let $L_{A,B}$ be the polynomial of degree $n-1$ verifying $\forall i\in[|1,n|],L_{A,B}(a_i)=b_i$. ($[|1,n|]=\{1,2,\dots,n\}$)

We know that this is a Lagrange interpolation polynomial and can be written $\displaystyle L_{A,B}(X)=\sum_{i=1}^n b_i\prod_{k=1,k

eq i}^n\dfrac{X-a_k}{a_i-a_k}$

However, that gives us a pretty 'abstract' definition of the polynomial. What is a good formula of the coefficient $C_k$ before $X^k$ in $L_{A,B}(X)$ ?