numerical methods – Lagrange polynomial interpolation, centered coefficients

My textbook says that Lagrange Interpolating on the interval $[a,b]$, with the data points $ (x_0, y_0), …, (x_n, y_n) $, written as:
$ prod_nf (x) = sum_ {i = 0} ^ ny_i phi_i (x) $with $ phi_i (x) $ being the polynomials of Lagrange, can also be written
$$ prod_nf (x) = sum_ {i = 0} ^ nc_i (x-m) ^ {n-i} $$
Or $ m = (a + b) / $ 2. I do not know how to calculate the coefficients $ c_i $. How is it done? I've just calculated the coefficients for $ n = $ 1.2but failed to establish a motive.