What is Associated Legendre polynomials

[Another1]

hey
i have doubt about Legendre polynomials and Associated Legendre polynomials
what is Associated Legendre polynomials ?
It different with Legendre polynomials ?

 

[Ackbach]

Associated Legendre polynomials are definitely different from Legendre polynomials (except when $m=0$ and $\ell\in\mathbb{Z}.$) The wiki articles are very helpful here, and I recommend you consult them.