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Linearization coefficients, orthogonal polynomials, and free probability
 

Summary: Linearization coefficients, orthogonal
polynomials, and free probability
Michael Anshelevich
February 15, 2005
{Hn(x)} = (monic) Hermite polynomials, orthogonal with
respect to the normal distribution
dľ(x) =
1

2
e-x2/2dx.
R
Hn(x) dľ(x) = n0,
R
Hn(x)Hk(x) dľ(x) = nkn!
What is
cn,k,l =
R
Hn(x)Hk(x)Hl(x) dľ(x)?
Why care:

  

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

 

Collections: Mathematics