Contour integral, exp(z^2)
1. The problem statement, all variables and given/known data Integrate exp(z^2) over the rectangle with vertices at 0, R, R + ia, and ia.
2. Relevant equations int(0, inf)(exp(x^2)) = sqrt(pi/2) 3. The attempt at a solution I really don't have much of an idea here  the function is analytic so has no residues... The part from 0 to R is just the real integral, but for the other 3 sides I'm not too sure on how to proceed. 
Re: Contour integral, exp(z^2)
Isn't the contour integral equal to 0 if there are no poles?

Re: Contour integral, exp(z^2)
Quote:
sqrt(pi)*exp(a^2)/2. 
Re: Contour integral, exp(z^2)

Re: Contour integral, exp(z^2)
Ah, that makes much more sense.
If we want to integrate from R+ia to ia, just integrate e^(z^2)dz=e^(x+ia)^2 dx from R to 0. Do the same for the other 3 sides. You won't get an analytic answer, but that's OK; just write out the entire contour integral first and you'll see where this is going. 
All times are GMT 5. The time now is 07:01 AM. 
Powered by vBulletin Copyright ©2000  2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums