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=====Associated Legendre Polynomials Lecture (20 minutes)=====

{{courses:lecture:cflec:central_forces_notes.pdf|Central Forces Notes}} Section 25

  * The Associated Legendre functions are defined and it is explained that these functions solve the general case in which m is not equal to 0. The Associated Legendre functions are not derived explicitly in the name of expediency. 
  * Some of the properties of the Associated Legendre functions are also demonstrated, including:
    * orthogonality and the inner product
    * the normalization constant is shown
    * the Rodriguez formula
    * the fact that for $m>\ell$, the Associated Legendre Polynomials are equal to 0.  This fact should be a one-step argument based on Rodriguez formula and is the basis for the restriction on the quantum numbers that $m<\ell$.

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