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May 4th, 2013, 01:12 PM   #1
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Computation of an integral.

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This problem was encountered here.

Subject: computation of the integral .



We will integrate the function (0<p<1) over the next figure.

[attachment=0:29xm8yvr]ikk.png[/attachment:29xm8yvr]



Letting and using the inequality



so . Since as , . So as we are left with,



and since the last two integrals converge absolutely we can omit the P.V. (principal value) and knowing that we get

.

So and for p=1/3 we get .
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