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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.

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# Hankel Transform.

Can you offer guidance or do you also need help?

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