:The standard practice of solving ( associate ) Legendre polynomial equation is power series method . The current Wiki article on that method is incomplete as it only pertains to nonsingular equations, which is almost useless when you encounter special functions.
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The power series method will give solutions only to initial value problems ( opposed to boundary value problems ), this is not an issue when dealing with linear equations since the solution may turn up multiple linearly independent solutions which may be combined ( by superposition ) to solve boundary value problems as well.
