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November 8th, 2012, 03:10 AM  #1 
Newbie Joined: May 2011 Posts: 22 Thanks: 0  Does this integration have a closeform result?
Hi guys, I have encountered a problem, the integral of following expression from 0 to : where $A>0,C>0, D>0$ are all positive constants, and $B>1$. Not sure there is closeform result for this integration. Maybe using Gamma function is also OK. Thanks for any solutions or hints!! 
November 8th, 2012, 06:30 AM  #2  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Does this integration have a closeform result? Quote:
 
November 8th, 2012, 04:49 PM  #3 
Newbie Joined: May 2011 Posts: 22 Thanks: 0  Re: Does this integration have a closeform result?
Hi, What is CA? Thanks. Jackson 
November 8th, 2012, 11:00 PM  #4 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Does this integration have a closeform result?
Complex Analysis. Use residue theorem.

November 9th, 2012, 12:20 AM  #5 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Does this integration have a closeform result?
I believe that this integral can be solved by hand using incomplete Gamma function.

November 9th, 2012, 02:58 AM  #6  
Newbie Joined: May 2011 Posts: 22 Thanks: 0  Re: Does this integration have a closeform result? Quote:
Hi zaidalyafey, Thanks for your reply. Could you show me how to use Gamma function to represent this? Or any detailed hint. I appreciate it sincerely. Jackson  
November 9th, 2012, 03:35 AM  #7 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Does this integration have a closeform result? 
November 11th, 2012, 08:12 PM  #8  
Newbie Joined: May 2011 Posts: 22 Thanks: 0  Re: Does this integration have a closeform result? Quote:
Hi @zaidalyafey Thanks a lot for this. I can see the former part of your last equation i.e., can be expressed by incomplete Gamma function. However, just wondering the latter part, i.e., can be represented similarly? Thanks a lot.  
November 12th, 2012, 02:30 AM  #9 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Does this integration have a closeform result? 
November 12th, 2012, 02:42 AM  #10 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Does this integration have a closeform result? 

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