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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


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    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.

    Thank you for your connection
  5. Jul 19, 2011 #4


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    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


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    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


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  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
    f=@(x)(1./(1+a*x.^2).*exp(i*k/(2*L)*(x.^2-2*x*r)));%% integral by numerical solution
  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
  15. Jul 20, 2011 #14
    Thanks, sorry for imposing on your thread!
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