Summary: Introduction to orthogonal polynomials
Michael Anshelevich
November 6, 2003
µ = probability measure on R with finite moments
mn(µ) =
R
xn dµ(x) < .
Induces a functional on polynomials C[x],
[P(x)] =
R
P(x) dµ(x).
On the polynomials C[x], define the sesquilinear inner
product
xn, xk
µ
= µ xn+k = mn+k(µ).
The set {xn}
n=0 is a basis for C[x]. Gram-Schmidt with
respect to the inner product ·, · µ, get a family of polyno-
mials

Source: Anshelevich, Michael - Department of Mathematics, Texas A&M University

Collections: Mathematics