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Mathematical method to get Laplacian]

Legendre Polynomials

<math>\Theta(\theta):\alpha,\beta = m^2</math>

where <math>\alpha</math> is separation of the r-dependent part and <math>\beta</math> is the separation of the <math>\phi</math> dependent part.

Then the Differential equation form of <math>\Theta(\theta)= P_l^m (cos\theta)</math> replacing <math>z=cos\theta</math>

is: <math>(1-z^2)\frac{d^2U}{dz^2} - 2z \frac{dU}{dz} + \alpha U = 0</math>

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