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Summary: Linearization coefficients for orthogonal
polynomials
Michael Anshelevich
February 26, 2003
Pn = monic polynomials of degree n = 0, 1, . . ..
{Pn} = basis for the polynomials in 1 variable.
Linearization coefficients: coefficients in the expansion of
Pn1Pn2 . . . Pnk
in the basis {Pn}.
For many classical families of orthogonal polynomials,
these are positive. For some examples, in fact positive
integers.
1
Let µ be a positive measure on R such that its moments
mn(µ) =
R
xndµ(x) < .
{Pn}
n=0 = Gram-Schmidt orthogonalization of {xn}
n=0.
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