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Orthogonality of free Sheffer systems Michael Anshelevich
 

Summary: Orthogonality of free Sheffer systems
Michael Anshelevich
August 5, 2004
= infinitely divisible probability measure, {t : t [0, )}
the corresponding convolution semigroup,
t s = t+s.
Assume all their moments are finite, centered, variance
1.
k(z) = log
R
exz d(x) = log

n=0
1
n!
mn()zn
is the cumulant-generating function, k(z) = 1
2z2 + . . ..
Let U = z+. . . be an analytic function / formal power se-
ries. The Sheffer polynomials (Sheffer 1937) are defined

  

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

 

Collections: Mathematics