Residue theorem to solve integration

Click For Summary
SUMMARY

The forum discussion focuses on solving the integral equation ∫1/[(z+ia)^2 *(z-ia)]*exp(-p^2[(A+iBz)/(C(z^2+a^2))])*exp(-ikbz)dz from the limits of 0 to l using the residue theorem. 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. The results plotted in MATLAB did not match expectations, indicating potential errors in the approach. The discussion highlights the importance of selecting the appropriate contour for evaluating residues at z=ia and z=-ia.

PREREQUISITES
  • Understanding of complex analysis, specifically residue theorem
  • Familiarity with integral calculus involving complex functions
  • Experience with MATLAB for plotting and numerical analysis
  • Knowledge of L'Hôpital's rule and its applications
NEXT STEPS
  • Research the application of the residue theorem in complex integration
  • Study contour integration techniques and their implications on residue calculations
  • Explore MATLAB's capabilities for complex function visualization and debugging
  • Learn about the conditions under which L'Hôpital's rule can be applied effectively
USEFUL FOR

Mathematicians, physicists, and engineers involved in complex analysis, particularly those working with integrals in the context of electromagnetic theory or wave propagation.

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?
 

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
3K
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
2K
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
2K
Solving Complex Integrals with Cauchy's & Residue Theorem
  • · Replies 5 ·
Replies
5
Views
2K