# 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 $$n = 1.2$$but failed to establish a motive.