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Jordan Lemma question

  1. Oct 4, 2007 #1
    Why I cannot use Jordan lemma to compute improper integral

    [tex]\int_{-\infty}^{\infty} f(z) \hbox{\ d}(z) [/tex]

    of a function like

    [tex] f(z)=\frac{\exp(-|z|)}{(a^2+z^2)} \mbox{\ for } a>0[/tex]

    Such a function is finite and continuous for [tex] |z|>a [/tex] and [tex] z f(z) [/tex] vanishes for [tex]z \to \infty[/tex].

    I know, that this function is not differentiable in z=0, but it seems to me that this is not a cause of problems, as there exists contour integral along the upper half-circle around the origin, and its limit for vanishing diameter is 0.

    Can somebody explain me why I cannot use Jordan lemma in this case?

    Thanks in advance,
    Cyril Fischer
  2. jcsd
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