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Hey! I have a question: how can you find the power-series solution and its leading term of the following ODE around the point x=+-(1-b) (where b is near x):

$$-(1-x^2)\frac{\partial^2 f^m_l}{\partial x^2}+2x\frac{f^m_l}{\partial x}+\frac{m^2}{1-x^2}f^m_l=l(l+1)f^m_l ,$$

and m and l are constants.

EDIT: Let me ask a better question - how can you find the solution to the following ODE:

$$ sin(\theta)\frac{\partial}{\partial \theta}(sin(\theta)\frac{\partial f(\theta)}{\partial \theta})+[l(l+1)sin^2(\theta)-m^2)]f(\theta)=0 $$

Thank you.

$$-(1-x^2)\frac{\partial^2 f^m_l}{\partial x^2}+2x\frac{f^m_l}{\partial x}+\frac{m^2}{1-x^2}f^m_l=l(l+1)f^m_l ,$$

and m and l are constants.

EDIT: Let me ask a better question - how can you find the solution to the following ODE:

$$ sin(\theta)\frac{\partial}{\partial \theta}(sin(\theta)\frac{\partial f(\theta)}{\partial \theta})+[l(l+1)sin^2(\theta)-m^2)]f(\theta)=0 $$

Thank you.

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