How to Integrate Bessel Functions Over z?

[besselevil]

Hi, I am trying to find the following integral of bessel functions, any help would be great:
∫H₀(z)²/z dz

Thanks

 

[Jorriss]

http://www.fh-jena.de/~rsh/Forschung/Stoer/besint.pdf

Perhaps this has the one you are looking for.

 

[besselevil]

Thanks but I have tried it and could not find it. Actually I am interested in integrals involving H₀(z)²/(z-a) or J₀(z)Y₀(z)/(z-a)

 

[JJacquelin]

The closed form involves very complicated special functions :
http://www.wolframalpha.com/input/?i=integrate+BesselH(0,x)^2*dx/x
If the denominator is (z-a) instead of z, I doubt that a closed form might exist with the standard special functions.

 

[besselevil]

The website is very useful, thanks a lot!

 

[Mute]

The closed form involves very complicated special functions :
http://www.wolframalpha.com/input/?i=integrate+BesselH(0,x)^2*dx/x
If the denominator is (z-a) instead of z, I doubt that a closed form might exist with the standard special functions.

Yeah, when I run into a Meijer-G function I usually take that as a sign that I want to solve the problem numerically (or, better yet, move on to another problem entirely. ).