Let X = {$P_1,P_2,P_3, \cdots P_k$} be a set of k distinct elements of a field. Define the function $Prod(j)$ = $\prod_{1 \leq i \leq k; i \neq j} \frac{1}{(P_j-P_i)}$. Then the following equation holds for an element $a$ in the field, given $a \neq P_1 \neq P_2\neq P_3 \cdots \neq P_k$:
$a^{(k-1)} = \frac{\sum_{1\leq j \leq k} P_j^{k-1} \times \frac{Prod(j)}{P_j-a}}{\sum_{1\leq j \leq k} \frac{Prod(j)}{P_j-a}}$
I am looking for a reference for this equation in the literature for this article https://arxiv.org/abs/2107.13520
Thanks in advance.