The — Classical Orthogonal Polynomials

∫abpn(x)pm(x)w(x)dx=hnδnmintegral from a to b of p sub n open paren x close paren p sub m open paren x close paren w open paren x close paren space d x equals h sub n delta sub n m end-sub is a normalization constant and δnmdelta sub n m end-sub

that satisfy an orthogonality condition with respect to a specific weight function over an interval . This condition is defined by the inner product: The Classical Orthogonal Polynomials

They are eigenfunctions of a differential operator of the form are polynomials of degree at most 2 and 1, respectively. ∫abpn(x)pm(x)w(x)dx=hnδnmintegral from a to b of p sub