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=== Analysis of the H polynomials ===
Let <math>\alpha_1,\dots,\alpha_n</math> be the roots of ''P(X)''. The so called Lagrange factors of ''P(X)'' are the cofactors of these roots,
:<math>P_m(X)=\frac{P(X)-P(\alpha_m)}{X-\alpha_m}.</math>
If all roots are different, then the Lagrange factors form a basis of the space of polynomials of degree at most ''n-1''. By analysis of the recursion procedure one finds that the H polynomials have the coordinate representation
:<math>
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