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- May 11th 2009, 07:45 PMsilversandLegendre Polynomial problem
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- May 16th 2009, 12:53 AMCaptainBlack
- May 16th 2009, 06:34 AMJester
I'm guessing what you mean is find not . From your BC, it's desirable to switch to polar coords, so your PDE becomes

with your BC

We'll shift the BC a bit by introducing so the PDE is the same but the new BCs is . Fortunately for us, this problem admits separable solutions so

Applying the boundary condtions gives us (we can set wlog)

which leads to the final solution

Side note: Title says Legendre polynomial - not sure why? They typically arise in 3D geometries but nothing in this post suggest that the problem is in .