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April 21st, 2010, 10:50 PM   #1
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Infinite series : 1/r^r

It is known that sigma(1/r^r) r=1,2,3.... = integral(1/x^x) limits 0 to 1.This is popularly known as the "Sophomore's dreams"
Now the value of this sum turns out to be 1.2912859... While searching for some relation between this sum and pi i stumbled upon this : 1 + 1/(pis+sqrt(pis^2+1))=1.29129 where pis=pi/2.
The two values differ only in the fifth decimal .
Could there be any possible link between the two ???
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April 22nd, 2010, 12:32 AM   #2
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Re: Infinite series : 1/r^r

Hello Zeefinity,

may be written as =
I don't quite know how to integrate this function, so if some-one could give us a hand on that one, we can see
whether Zeefinity's statement is right.

Hoempa
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April 22nd, 2010, 05:13 AM   #3
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Re: Infinite series : 1/r^r

I searched the net regarding that integral and found out that it is a non integrable function whose integral cannot be expressed in terms of elementary functions.
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April 22nd, 2010, 05:25 AM   #4
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Re: Infinite series : 1/r^r

I tried in in Geogebra as well. It gave a questionmark when I tried it. Too bad.

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August 28th, 2011, 11:18 PM   #5
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Re: Infinite series : 1/r^r

Hello !

This is a link to a paper dealing with the integral of x^x :
http://www.scribd.com/people/documents/ ... jjacquelin
Then select "Sophomores Dream Function".
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