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G(x1+x2)=\sum g(a_{i,j}x^ix^j)

  1. Aug 4, 2009 #1
    I wonder in what circumstances:

    given a function g, we can analytically find the coefficients [tex]a_{i,j}[/tex]

    [tex]g(x1+x2)=\sum a_{i,j}g(x^ix^j)[/tex]

    I'm not if this would server any useful applications but the transformation looks interesting to me. It looks very simmilar to a polynomial transformation.
     
  2. jcsd
  3. Aug 5, 2009 #2
    For an arbitrary function g(x), I doubt it. There might be a family of functions though.
     
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