Solve Complicated Integral: Get Professional Help

Canerg
Messages
12
Reaction score
0
Hi this is very complicated integral i couldn't solve
can you help me ? how does it solve
 

Attachments

Physics news on Phys.org
Hello, is j negative, and do you know if a is non-zero or positive? I think this integral only exists if j is non-positive and a is non-negative.
 
Last edited:
j=sqrt(-1) and a is positive
I solved this integral numerically and i found the exact result in both Matlab and Mathematica program but I need analytical solution. I tried residue theorem but result didn't match numeric solutions.I asked some mathematicians but they couldn't find true path for the residue and i look ryzik integral book i coulnd't find.

sqrt;squareroot
Thank you for your connection
 
Calculus of residues perhaps?
 
yes Calculus of residues but true path is important
may be fresnel integral can solve this problem but diffucult to understand. :(
 
You could complete the square and see if that might help you.

What do you mean by true path?
 
can you help me to solve using square
 
x^{2}-2rx=(x-r)^{2}-r^{2}
 
:) ok
i will try
 
  • #10
What program did you write those equations in if you don't mind Canerg?
 
  • #11
Hi BackEMF this is my Matlab code you can use quad instead of quade

%clc; clear all
lamda=1.55e-6;
k=2*pi/lamda;
a=10000;
r=1e-2;L=1000;
f=@(x)(1./(1+a*x.^2).*exp(i*k/(2*L)*(x.^2-2*x*r)));%% integral by numerical solution
numerical=quade(f,-inf,inf)
 
  • #12
Hi Canerg, sorry I wasn't clear enough. I meant the equations you submitted in PDF, do you mind telling me what typsetting program did you use?
 
  • #13
MathType5
 
  • #14
Thanks, sorry for imposing on your thread!
 
Back
Top