Monday Math 42

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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One Response to “Monday Math 42”

  1. Monday Math 112 « Twisted One 151's Weblog Says:

    […] 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, […]

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