integral of spherical bessel function (first kind), first order

efrenfer

Hello,
I am trying to solve the following integral (limits from 0 to inf).

∫j_1(kr) dr

where j_1 is the first order SPHERICAL Bessel function of the first kind, of argument (k*r). Unfortunately, I cannot find it in the tables, nor manage to solve it... Can anybody help?

Thanks a lot! Any help will be very appreciated.

P.S: I came across this integral trying to apply analytically a direct filtering operation (convolution) in space domain to a point source (in a 3D space).

JJacquelin

Thanks to WolframAlpha :

Attached Thumbnails

 

efrenfer

Alright! Thanks a lot!