Legendre polynomials and Associated Legendre polynomials.
v = plegendre(L,x) v = plegendre(L,M,x)
With two input arguments,
plegendre
returns the value(s) of the Legendre
polynomal of degree L (with L ≥ 0).
With three input arguments,
the value(s) of the associated Legendre
polynomal of degree L (with L ≥ 0) and order M (with |M| ≤ L)
are returned.
x
must satisfy -1≤ x ≤ +1 and can be a scalar or an array.
plegendre
is using recurrence relations to compute the
values, as described in Press et al, Numerical Recipes in C++ (2002).
Note that contrary to that reference, but in line with most others,
the Condon-Shortley phase factor (-1)^m is not included in plegendre
.
It is included in the spherical harmonics computed by
spherharm.
clebschgordan, spherharm, wigner3j, wigner6j