Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Improper integral

  1. Jul 19, 2011 #1
    Hi this is very complicated integral i couldn't solve
    can you help me ? how does it solve
     

    Attached Files:

  2. jcsd
  3. Jul 19, 2011 #2

    disregardthat

    User Avatar
    Science Advisor

    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: Jul 19, 2011
  4. Jul 19, 2011 #3
    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
     
  5. Jul 19, 2011 #4

    hunt_mat

    User Avatar
    Homework Helper

    Calculus of residues perhaps?
     
  6. Jul 19, 2011 #5
    yes Calculus of residues but true path is important
    may be fresnel integral can solve this problem but diffucult to understand. :(
     
  7. Jul 19, 2011 #6

    hunt_mat

    User Avatar
    Homework Helper

    You could complete the square and see if that might help you.

    What do you mean by true path?
     
  8. Jul 19, 2011 #7
    can you help me to solve using square
     
  9. Jul 19, 2011 #8

    hunt_mat

    User Avatar
    Homework Helper

    [itex]x^{2}-2rx=(x-r)^{2}-r^{2}[/itex]
     
  10. Jul 19, 2011 #9
    :) ok
    i will try
     
  11. Jul 19, 2011 #10
    What program did you write those equations in if you don't mind Canerg?
     
  12. Jul 20, 2011 #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)
     
  13. Jul 20, 2011 #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?
     
  14. Jul 20, 2011 #13
    MathType5
     
  15. Jul 20, 2011 #14
    Thanks, sorry for imposing on your thread!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Improper integral
  1. Improper integral (Replies: 1)

  2. Improper Integration (Replies: 5)

  3. Improper integrals (Replies: 4)

  4. Improper Integrals (Replies: 1)

  5. "Improper" Integral (Replies: 3)

Loading...