Prove...

please help...

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- Dec 30th 2012, 10:23 PMOzymandiasVardi's Integral
Prove...

please help... - Dec 30th 2012, 11:12 PMsbhatnagarRe: Vardi's Integral
The evaluation of such integrals involves a lot of number theory. We will need the Dirichlet L Function

The gamma function,

Now let

Differentiate with respect to the parameter .

Hence we conclude

Evaluating is it not a "walk in the park" and requires the help of number theory.