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Delta function (hard question)

  1. Sep 2, 2013 #1
    1. The problem statement, all variables and given/known data
    Compute ∫[itex]^{∞}_{-∞}[/itex]dx (x2+a2)-1δ(sin(2x)), without calculating the resulting sum.


    2. Relevant equations

    This is a very specific integral which ,has a delta function δ operating on sin function

    3. The attempt at a solution
    Does anyone know this integral ? I haven't seen before any similar examples.
     
  2. jcsd
  3. Sep 2, 2013 #2

    vanhees71

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    2016 Award

    You haven't listed all relevant equations yet:
    [tex]\delta[f(x)]=\sum_{k} \frac{1}{\left |f'(x_k) \right|} \delta(x-x_k),[/tex]
    where [itex]x_k[/itex] runs over all zeros of [itex]f[/itex], which all must be simple zeros of course in order that [itex]f'(x_k) \neq 0[/itex] for all [itex]k[/itex].
     
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