Evaluating the integral of e^(-j√(x²+a²))e^(-jkx) from -∞ to ∞

[CuppoJava]

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

 

[JJacquelin]

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).

 

[JJacquelin]

A typo in your integral ?