## Christoffel-Darboux Formula

For three consecutive Orthogonal Polynomials

 (1)

for , 3, ..., where , , and are constants. Denoting the highest Coefficient of by ,
 (2) (3)

Then

 (4)

In the special case of , (4) gives

 (5)

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 785, 1972.

Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., pp. 42-44, 1975.