Help getting started with this integral

  • Thread starter Thread starter CuppoJava
  • Start date Start date
  • Tags Tags
    Integral
CuppoJava
Messages
23
Reaction score
0
Hello everyone,

I'm having trouble understanding how to evaluate this integral. I am not sure whether there is a closed form solution.

\int_{-\infty}^\infty e^{-j\sqrt{x^2+a^2}} e^{-jkx} dx

I am trying to express a polar wave as a summation of plane waves, and this integral drops out when solving for the amplitudes of the plane waves. Thanks very much for your help. A link to a reference, or the necessary techniques would be very helpful.

-Patrick
 
Physics news on Phys.org
Hi !

Did you first check if the integral is convergent or not ?
If not, are you sure that the given integral has a physical meaning ?
(I think that the integral is not convergent).
 
A typo in your integral ?
 

Attachments

  • Fourier transform.JPG
    Fourier transform.JPG
    11 KB · Views: 435
Back
Top