Residue theorem to solve integration

Click For Summary
The discussion revolves around solving a complex integral using the residue theorem, specifically the integral of a function involving exponential terms and poles at z=ia and z=-ia. The user encountered difficulties due to the complexity introduced by the factors in the exponential term and attempted to apply L'Hôpital's rule without success. Despite efforts to solve the integral, the resulting plot in MATLAB did not match expectations, indicating a potential error in the approach. Participants are seeking clarification on the appropriate contour to use for evaluating the residues. The conversation highlights the challenges of applying the residue theorem in complex integrals.
Elsasw
Messages
10
Reaction score
0
Hi all, i have an integral equation of

∫1/[(z+ia)^2 *(z-ia)]*exp(-p^2[(A+iBz)/(C(z^2+a^2))])*exp(-ikbz)dz

from the limit of 0 t0 l

I tried perform residue theorem but due to the 1/[(z+ia)(z-ia)] factor in the exponential term complicated it...I also tried incorporate L'Hopita rules in the exp term. I did manage to solve it but did not seems to be right because when i plotted in with Matlab, the plot is not correct. Perhaps my approach is wrong.

Need advise to solve this again.
Thank you
 
Physics news on Phys.org
What contour were you using?
 
HallsofIvy said:
What contour were you using?

Contour? Does this referred to residues at z=ia and z=-ia?
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

How to find the residue of a complex function
  • · Replies 14 ·
Replies
14
Views
3K
Complex Integration using residue theorem
  • · Replies 1 ·
Replies
1
Views
2K
Residue Theorem applied to a keyhole contour
  • · Replies 23 ·
Replies
23
Views
2K
Complex Integration Along Given Path
  • · Replies 3 ·
Replies
3
Views
2K
Can I Use Substitution to Prove the Residue Theorem Integral?
  • · Replies 5 ·
Replies
5
Views
1K
Compute the residue of a function
  • · Replies 2 ·
Replies
2
Views
2K
Residue Theorem: Finding the Integral of z^3e^(-1/z^2) over |z|=5
  • · Replies 6 ·
Replies
6
Views
2K
Calculating Integral Using Residue Theorem & Complex Variables
  • · Replies 4 ·
Replies
4
Views
2K
Find the residues of the following function + Cauchy Residue
  • · Replies 2 ·
Replies
2
Views
1K
Solving Complex Integrals with Cauchy's & Residue Theorem
  • · Replies 5 ·
Replies
5
Views
2K