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.


Tags: , , , , ,

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, […]

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s

%d bloggers like this: