Find .

Here, we use integration by parts, with and ; then and

Now, using and , integration by parts tells us:

.

Now, we proved here that , so the above is just this for the case *n*=2, so since and (see here), then our integral is

.

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Tags: Gamma Function, Hyperbolic Sine, Integration, Integration by Parts, Math, Monday Math, Riemann Zeta Function

This entry was posted on June 29, 2009 at 1:46 am and is filed under Math/Science. You can follow any responses to this entry through the RSS 2.0 feed.
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July 13, 2009 at 12:05 am |

[…] , so that ; v=0 when r=1, and v→∞ when r=0. Thus, our integral becomes And we found here that this equals […]