# Elliptic Integrals

by boarie
Tags: elliptic, integrals
 Sci Advisor HW Helper P: 11,915 Here's the trick. U need to use some notations $$R^{2}+r^{2} =p^{2}$$ $$2rR\sin\vartheta =u$$ One has that $p^2 >0 \ ,\ u>0$. Then the integral becomes $$B_{r}(r,\vartheta) =C \int_{0}^{2\pi} \frac{d\phi}{\left(p^{2}-u \sin\phi\right)^{\frac{3}{2}}} = C$$ times the result below. The notation for the complete elliptic integrals is the one Mathematica uses. U can check it out on the Wolfram site and compare it to the standard one (for example the one in Gradshteyn & Rytzik). Daniel.