What is the value of the integral ? How about the general , for non-negative integer *n*?

First, recall that . Thus,

Recall from the previous Monday Math post the digamma function: ,

and thus

.

In particular, , with *γ* the Euler-Mascheroni constant.

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Tags: Digamma Function, Euler-Mascheroni, Gamma Function, Integration, Math, Monday Math

This entry was posted on October 20, 2008 at 12:01 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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March 15, 2010 at 12:14 am |

[…] Making the u-substitution u=st, we get . Now, one may recall that we found the remaining integral here: , where γ is the Euler-Mascheroni constant. Thus, […]