Monopole and Dipole Terms of Electric potential (V) on Half Disk

jkthejetplane
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Homework Statement
So this is from my last exam. I wanted to figure this out as we can get some credit back on a question plus finals are coming up.
Relevant Equations
On my attached attempt you can see the equations I use as well as a few of the professor's notes
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Calculate potential on the z axis in terms of a Legendre polynomials. Then the off axis expansion will follow.
 

Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW
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