For example:L[x0,x1,...,xn;f+g]=?=L[x0,x1,...,xn;f] + L[x0,x1,...,xn;g] where f and g are ordinary functions, not neccessarily polynomials......


closed as unclear what you're asking by TheSimpliFire, i. m. soloveichik, Chris Godsil, José Carlos Santos, Mohammad Riazi-Kermani Feb 20 '18 at 0:03

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If $L[x_0, \ldots, x_n; f]$ means a polynomial of degree $ \le n$ that has the same values as $f$ at $x_0, \ldots, x_n$, then yes, this is true.

  • $\begingroup$ so in my case f:=x^n+x^(n-1)+...+1 and g:= -1/(x+1) and I want to calculate L[x0,x1,...,xn; f+g] but I don't know how I should do it..... $\endgroup$ – Nfff3 Feb 19 '18 at 20:23
  • 1
    $\begingroup$ $f$ is already a polynomial of degree $n$, so its interpolating polynomial is itself. $\endgroup$ – Robert Israel Feb 19 '18 at 20:32
  • $\begingroup$ yes, I agree, but what about g? $\endgroup$ – Nfff3 Feb 19 '18 at 21:22

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