Differential Equation
Associated Legendre functions are solutions of the Legendre equation
where the complex numbers λ and μ are called the degree and order of the associated Legendre functions respectively. Legendre polynomials are the associated Legendre functions of order μ=0.
This is a second order linear equation with three regular singular points (at 1, −1, and ∞). Like all such equations, it can be converted into the hypergeometric differential equation by a change of variable, and its solutions can be expressed using hypergeometric functions.
Read more about this topic: Legendre Function
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