Wondered why -2

This is the second post in the series of Wondered Why?

Did you think why we as Electronics and Communication engineers studied Legendre’s Polynomials. These were formulated or rather discovered by Adrien Marie Legendre a Paris born French Mathematician in the late 18th century. What does it have to do with Electronics then, which was discovered long time after his discovery?

Well, like Bessel’s Function(my previous post) the legendre’s polynomials appear in the solution of Laplace equation for potential in charge free space

\nabla^2 \Phi(\mathbf{x})=0

the solution when it is solved using separation of variables comes out to be

<br />
\Phi(r,\theta)=\sum_{\ell=0}^{\infty} \left[ A_\ell r^\ell + B_\ell r^{-(\ell+1)} \right] P_\ell(\cos\theta).<br />

A_\ell and B_\ell are to be determined according to the boundary condition of each problem.

Thus Legendre’s Polynomials find their application in Electrostatics.

This ends the second part. Wait for the next one.

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