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Lagranges interpolation

  1. Oct 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Let D:R[x]->R[x]be the differentiation operator D(f(x))=f'(x),prove that
    e^tD(f(x))=f(x+t) for a real number t

    2. Relevant equations

    application of Lagranges interpolation



    3. The attempt at a solution
    i dont know how to begin or construct the proof here
     
  2. jcsd
  3. Oct 25, 2012 #2

    Dick

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    You didn't write that very grammatically. You mean e^(tD)(f(x))=f(x+t). Write out a Taylor series expansion of f(x+t) around x. Now compare it with e^(tD)=1+tD+(t^2)D^2/2!+(t^3)D^3/3!+... acting on f(x).
     
  4. Oct 25, 2012 #3

    lurflurf

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    There are many ways, through most are not rigorous.

    One way is to expand both side in Taylor series in t.
     
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