Let be an th degree Polynomial with zeros at , ..., . Then the fundamental
Polynomials are

(1) 
They have the property

(2) 
where
is the Kronecker Delta.
Now let , ..., be values. Then the expansion

(3) 
gives the unique Lagrange Interpolating Polynomial assuming the values at . Let
be an arbitrary distribution on the interval , the associated Orthogonal
Polynomials, and , ..., the fundamental Polynomials corresponding to the
set of zeros of . Then

(4) 
for , 2, ..., , where are Christoffel Numbers.
References
Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI:
Amer. Math. Soc., pp. 329 and 332, 1975.
© 19969 Eric W. Weisstein
19990526