The Spherical Harmonics are
where the
Introducing
x cos
, the associated Legendre Polynomials Plm
solve the differential equation
They are related to the ordinary Legendre Polynomials by
which are given by the Rodrigues formula
Note our Ylm are identical to those of Edmonds (1957) [6], even though our definition of the Plm differ by a factor (- 1)m.
Eric Hivon 2003-02-07