I found this passage in a book:(adsbygoogle = window.adsbygoogle || []).push({});

http://img8.imageshack.us/img8/1452/75717730.jpg [Broken]

where Φ(x) is the c.d.f. of the normal distribution.

However, using integration by parts I also get this term which is not included in the passage:

[tex] [ e^{itx} \phi(x) ]^{+ \infty}_{- \infty} [/tex]

where i is the imaginary unit and [tex] \phi(x) [/tex] is the normal p.d.f.

So,

[tex] e^{itx} \phi(x) = \frac{1}{\sqrt{2\pi}} \exp \left( -0.5x^2 + itx \right) [/tex]

So, is this term:

[tex] \left[ \frac{1}{\sqrt{2\pi}} \exp \left( -0.5x^2 + itx \right) \right]^{+ \infty}_{- \infty} [/tex]

equal to zero and why? It is not clearly evident to me

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# Integration by parts

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