Evaluate .

How many methods you know to solve it?

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- Jan 1st 2008, 07:48 AMJemLogarithm integral
Evaluate .

How many methods you know to solve it? - Jan 1st 2008, 08:19 AMThePerfectHacker
- Jan 1st 2008, 10:12 AMgalactus
This particular integral is related to what is known as the 'dilogarithm'.

In our case,

It seems to me there is also a unit disk reference with the dilog. It says for n=2 and z in the unit disk, then

i.e, if z=1, then we have

There is also a trilogarithm. - Jan 1st 2008, 10:33 AMbobak
what is dilog galactus?

- Jan 1st 2008, 11:04 AMgalactus
Do a google to find out more. It is a cool function with lotsa implications.

For instance, it has the series:

Also,

In the event z = -1, then we have what PH posted.

Notice how the Basel sum is involved here.

I noticed the similarity between this and the posters integral and thought there was a connection. I am sure Wiki or Mathworld has something about it.

The dilog is the polylog with n=2. There are others. As I mentioned, a trilog.

It has implications to gamma and other things. Research it. You'll find it cool. - Jan 18th 2008, 08:31 AMKrizalid
- Jan 18th 2008, 08:35 AMThePerfectHacker