What Are the Applications of Associated Legendre Functions?

[BCox]

Hello:

What are Associated Legendre functions? What are they good for in terms of applications?

 

[James Leighe]

I think it's used in solving partial differentials in a Riemann (complex) sphere, though not all pde's relating to physics can be visualized in a Riemann sphere... few actually.

But some can, like the evolution of the electric and magnetic fields!


('I think' being operative here, someone with more experiences with this could answer more clearly and probably more correctly)

 

[BCox]

ok. In what time of application or simply why would we multiply Associated Legendre with another function and then integrate over the real line?