Physics Help Forum theorem of residues

 General Physics General Physics Help Forum

 Oct 1st 2009, 11:24 PM #1 Senior Member   Join Date: Sep 2009 Location: india Posts: 409 theorem of residues the theorem about sum of residues tells us that the integral f(z)dz around a closed curve in complex plane containing many singular points is equal to 2 pi i times the sum of the residues calculated at each singular point.in the proof we make cuts and apply cauchy integral theorem in each and then add.then why is it not (n)times the integral f(z)dz=2pi i times sum of resiodues. where 'n' is the no of singular points.
 Oct 3rd 2009, 10:38 AM #2 Senior Member   Join Date: Jul 2009 Location: Kathu Posts: 131 theorem of residues For one thing, the integrals round the non analytic points can be different to 2*pi*i for example it could be 3*pi*i for one and 0.5*pi*i for another. So although the idea is the same, you need to take the behaviour of each individual point into account using it's Laurent series I think.
 Oct 4th 2009, 12:13 AM #3 Senior Member   Join Date: Sep 2009 Location: india Posts: 409 a possible solution i think i was wrong. i thought the cuts were made one at a time with individual singular points. but the story is that all cuts are made the same time, so the the integration is a tangled mess of paths but on the brighter side, the main integration of f(z)dz comes into account only once throught the outermost contour. have i got it right?
 Oct 4th 2009, 01:21 AM #4 Physics Team   Join Date: Feb 2009 Posts: 1,425 Why dont you post this in the math help forum also? You are bound to get a faster response there. ( im really rusty with this stuff.)

 Tags residues, theorem

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post teslacosmathematicas Theoretical Physics 2 Jun 17th 2013 07:02 AM maple_tree Advanced Electricity and Magnetism 11 Dec 10th 2010 11:26 AM r.samanta Energy and Work 3 Nov 29th 2009 11:04 PM r.samanta Electricity and Magnetism 2 Oct 1st 2009 11:12 PM muuusen Electricity and Magnetism 1 Mar 31st 2009 11:20 PM