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November 8th, 2012, 02:10 AM | #1 |
Newbie Joined: May 2011 Posts: 22 Thanks: 0 | Does this integration have a close-form 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 close-form result for this integration. Maybe using Gamma function is also OK. Thanks for any solutions or hints!! |
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November 8th, 2012, 05:30 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 close-form result? Quote:
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November 8th, 2012, 03:49 PM | #3 |
Newbie Joined: May 2011 Posts: 22 Thanks: 0 | Re: Does this integration have a close-form result?
Hi, What is CA? Thanks. Jackson |
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November 8th, 2012, 10:00 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 close-form result?
Complex Analysis. Use residue theorem.
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November 8th, 2012, 11:20 PM | #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 close-form result?
I believe that this integral can be solved by hand using incomplete Gamma function.
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November 9th, 2012, 01:58 AM | #6 | |
Newbie Joined: May 2011 Posts: 22 Thanks: 0 | Re: Does this integration have a close-form 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 | |
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November 9th, 2012, 02:35 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 close-form result? |
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November 11th, 2012, 07:12 PM | #8 | |
Newbie Joined: May 2011 Posts: 22 Thanks: 0 | Re: Does this integration have a close-form 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. | |
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November 12th, 2012, 01:30 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 close-form result? |
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November 12th, 2012, 01:42 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 close-form result? |
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