Summary: arXiv:math.CO/0311043
Free Appell polynomials
Michael Anshelevich
March 2, 2004
µ = probability measure on R, all of whose moments
mn(µ) =
R
xn dµ(x) < .
Many polynomial families {Pn}
n=0 associated to it. All
satisfy P0(x) = 1,
Pn, 1 =
R
Pn(x) dµ(x) = 0
for n > 0.
1) Orthogonal polynomials:
Pn, Pk =
R
Pn(x)Pk(x) dµ(x) = n,k.
Example: Hermite, Laguerre, Charlier, Jacobi, Cheby-

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

Collections: Mathematics