April 21st, 2010, 10:50 PM  #1 
Newbie Joined: Apr 2010 Posts: 16 Thanks: 0  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 ??? 
April 22nd, 2010, 12:32 AM  #2 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Infinite series : 1/r^r
Hello Zeefinity, may be written as = I don't quite know how to integrate this function, so if someone could give us a hand on that one, we can see whether Zeefinity's statement is right. Hoempa 
April 22nd, 2010, 05:13 AM  #3 
Newbie Joined: Apr 2010 Posts: 16 Thanks: 0  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.

April 22nd, 2010, 05:25 AM  #4 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Infinite series : 1/r^r
I tried in in Geogebra as well. It gave a questionmark when I tried it. Too bad. Hoempa 
August 28th, 2011, 11:18 PM  #5 
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8  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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