August 5th, 2012, 10:49 PM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Improper Gamma Integral
Okay, I know that and both diverges. But what about this limit: ? Is this also divergent? Or is it convergent? Even if I had a graph of , It would mean a lot to me. Can anybody give me a graph?(Oh, I know that's not possible ) Any help will be greatly appreciated. Balarka . 
August 6th, 2012, 12:34 AM  #2 
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8  Re: Improper Gamma Integral
Hi ! I think that F(n) is not converging because, for n tending to infinity, the Sum is equivalent to Gamma(n) and the Integral is equivalent to Gamma(n)/ln(n)) 
August 6th, 2012, 12:39 AM  #3  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Improper Gamma Integral Quote:
 
August 6th, 2012, 06:51 AM  #4  
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8  Re: Improper Gamma Integral Quote:
 
August 6th, 2012, 06:53 AM  #5 
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8  Re: Improper Gamma Integral
&............................

August 6th, 2012, 10:03 AM  #6 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Improper Gamma Integral
Ok. Lots of Thanks, Balarka . 
August 6th, 2012, 10:57 AM  #7 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Improper Gamma Integral
I found another interesting thing about : It is well known that: Now, the euler's reflection formula for the gamma function states that: Substituting this into (1) gives From this, So, F(1x) diverges for all I am currently very sleepy now so please forgive me if I am wrong Balarka . 

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