
Complex Analysis Complex Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 14th, 2012, 10:50 AM  #1 
Senior Member Joined: May 2011 Posts: 501 Thanks: 6  another somewhat challenging contour integral?.
Here's another integral I ran across. I thought perhaps a rectangular contour may be in order, but turns out maybe a semicircular one after all?. I tried rewriting it as cosh has an infinite number of poles . is a pole of as well as for cosh(x). Anyone have a good method for this one?. I am not certain I am doing it correctly due to cosh and the rational part having poles at the same place. Namely, . Here is a link to a similar problem: http://129.81.170.14/~vhm/papers_html/final21.pdf The residue at they get . I get close, but I do not know from where they get that residue. They do not explain...just show it. 
May 15th, 2012, 10:37 AM  #2 
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: another somewhat challenging contour integral?. 
May 15th, 2012, 11:44 AM  #3 
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: another somewhat challenging contour integral?.
...

May 15th, 2012, 01:39 PM  #4 
Senior Member Joined: May 2011 Posts: 501 Thanks: 6  Re: another somewhat challenging contour integral?.
If we make the sub in the original integral, we get: cosh and both have a pole at x=i and cosh at For i the residue is Multiply by the and we get The other 0's of cosh are at . Where k=0 would correspond to i, the one we just found. So, for the other poles for k=1,2,3,.... the residues are at Taking the sum, beginning at 1, and summing them up we get: Now, do not forget to add the k=0 for i from before and we get: Since this is an even function, divide by 2 and get 

Tags 
challenging, contour, integral 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Contour integral  mathematician1234  Complex Analysis  1  November 23rd, 2013 02:16 AM 
Contour integral  evol_w10lv  Real Analysis  2  September 15th, 2013 01:31 AM 
help on contour integral!  qwertyuiop89  Complex Analysis  1  November 20th, 2012 07:32 AM 
contour integral with sin and e  galactus  Complex Analysis  9  May 22nd, 2012 03:38 AM 
Contour integral  evol_w10lv  Calculus  0  December 31st, 1969 04:00 PM 