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Introduction to orthogonal polynomials Michael Anshelevich
 

Summary: Introduction to orthogonal polynomials
Michael Anshelevich
November 6, 2003
= probability measure on R with finite moments
mn() =
R
xn d(x) < .
Induces a functional on polynomials C[x],
[P(x)] =
R
P(x) d(x).
On the polynomials C[x], define the sesquilinear inner
product
xn, xk

= xn+k = mn+k().
The set {xn}
n=0 is a basis for C[x]. Gram-Schmidt with
respect to the inner product , , get a family of polyno-
mials

  

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

 

Collections: Mathematics