September 1st, 2012, 10:15 PM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Divergence and Asymptotes 1. Prove or disprove : diverges. 2. Prove or disprove : has an asymptote. Thank you for any help, Balarka . 
September 2nd, 2012, 01:17 AM  #2 
Senior Member Joined: May 2011 Posts: 501 Thanks: 6  Re: Divergence and Asymptotes
HI mathbalarka: I assume is the polylogarithm?. The polylog is defined as But the problem simply states . Perhaps I am misunderstanding, but which particular polylog is to be used?. In this case, it would be x=1 and mean . Then, we would have the limit as part of the problem?. Another notation would be i.e. the dilogarithm: which, when x=1, would be the classic . In other words, we have to know which polylog we are dealing with. My apologies if I am not getting something obvious. 
September 2nd, 2012, 01:27 AM  #3 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Divergence and Asymptotes
No, is the offset logarithmic integral 
September 2nd, 2012, 01:30 AM  #4 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Divergence and Asymptotes
For 1, proving it disproving it diverges would probably use a technique similar to proving the EulerMascheroni constant converges. I don't know how to do that. It would be somehow showing that diverges. The EulerMascheroni constant has x in place of log(x). The differences probably do not decrease fast enough as it's logarithmic.


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