Why I cannot use Jordan lemma to compute improper integral(adsbygoogle = window.adsbygoogle || []).push({});

[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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Jordan Lemma question

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**