Hey guys,(adsbygoogle = window.adsbygoogle || []).push({});

Do you have any advice of a place for learning about Hankel's Transform and its application to Laplace Equation?.

There are a couple of lines of a paper in which I am stuck on, I don't know how do they do this stuff:

Defining the operator [tex]L_m^2=\frac{1}{r}\frac{\partial}{\partial r}

\left(r\frac{\partial}{\partial r}\right)-\frac{m^2}{r^2}+\frac{\partial^2}{\partial z^2}[/tex]

then the solution of [tex]L_m^2 f=0[/tex] under the bipolar change of variables [tex]r=2\eta/(\eta^2+\xi^2)[/tex] and [tex]z=2\xi/(\eta^2+\xi^2)[/tex] is given by:

[tex]f=(\xi^2+\eta^2)^{1/2}\int_0^\infty(A(s)sinh(s\xi)+B(s)cosh(s\xi))J_m(s\eta)ds[/tex]

I have tried to perform the change of variables in the differential operator, but it turns out to be the Hell when doing that for the second derivative. Any advice?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Hankel Transform.

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**