Spherical harmonic conventions
The Spherical Harmonics are defined as
where the
Introducing
, the associated Legendre Polynomials P_{lm}
solve the differential equation


0. 
(23) 
They are related to the ordinary Legendre Polynomials P_{l} by
P_{lm} 


(24) 
which are given by the Rodrigues formula
P_{l}(x) 


(25) 
Note our Y_{lm} are identical to those of [Edmonds, 1957],
even though our definition of the P_{lm} differ from his by a factor
(1)^{m} (a.k.a. CondonShortley phase).
Eric Hivon
20100618
