(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In 2D: (del^{2}+ k^{2}) u(r,theta) = 0 with b.c u(R,theta) = f(theta)

Starting from the general solution (by separation of variables) show that the solution can be rewritten as:

[tex]\int[/tex] K(r,theta,theta')*f(theta') dtheta' from 0 to 2*Pi

2. Relevant equations

The general solution is J_{m}(k*r)*P_{m}(cos(theta)) where P_{m}are the Legendre polynomials and J_{m}are the Bessel functions

3. The attempt at a solution

Ok so I've attempted this on three different occasions, following the professor's instructions to the problem I end up with a relationship J_{m}(kR) P_{m}(cos(theta)) = f(theta) where I need to find the values for k, but this would require some type of inversion for the Bessel functions. So I am thinking this isn't the case.

Alternatively, if I try to define the solution u(r,theta) = v(theta) + w(r,theta) I end up getting confused on how to properly deal with the v(theta) term. I know it needs to obey the boundary conditions so I can rewrite the equation as an inhomogeneous helmholtz equation in terms of w(r,theta) and then find the solution as an integral involving the appropriate Green's function.

Any help?

**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!

# Homework Help: Helmholtz Equation with non-homogeneous b.c.

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

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