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Linearization coefficients for orthogonal polynomials using stochastic
 

Summary: Linearization coefficients for orthogonal
polynomials using stochastic
processes
Michael Anshelevich
March 6, 2003
{Pn} = basis for the polynomials in 1 variable.
Linearization coefficients: coefficients in the expansion of
Pn1Pn2 . . . Pnk
in the basis {Pn}.
When {Pn} are orthogonal,
Pn1Pn2 . . . Pnk =

m=0
1
P2
m
Pn1Pn2 . . . PnkPm Pm,
where is the expectation with respect to the orthogo-
nality measure,
F = F(x)d(x).

  

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

 

Collections: Mathematics