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Orthogonal polynomials and counting permutations Michael Anshelevich
 

Summary: Orthogonal polynomials and counting permutations
Michael Anshelevich
f = some function. Orthogonal polynomials with respect to f:
Pn(x)Pk(x)f(x) dx = 0 if n = k,
Example.
1
-1
Pn(x)Pk(x) dx = 0 if n = k
Legendre
P0 = 1,
P1 = x,
P2 = x2 -
1
3
,
P3 = x3 -
3
5
x, etc.
1

  

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

 

Collections: Mathematics