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Newton's formula for interpolation is

$$P(x)=c_1+c_2(x-x_1)+c_3(x-x_1)(x-x_2)+c_4(x-x_1)(x-x_2)(x-x_3)+\cdots$$

I prefer sigma notation, when it is possible. Can this be written in sigma notation?

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You can write $\displaystyle P(x)= \sum\limits_{i=1}^{+ \infty} c_i \prod\limits_{j=1}^{i-1} (x-x_j)$, with the convention $\prod\limits_{j=1}^0 (x-x_j)=1$.

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