Legendre polynomials and associated Legendre polynomials.
v = plegendre(L,z) v = plegendre(L,M,z) v = plegendre(L,M,z,CSphase)
With two input arguments, plegendre
returns the value(s) of the Legendre polynomial of degree L (with L ≥ 0).
With three or four input arguments, plegendre
calculates the value(s) of the associated Legendre polynomial of degree L (with L ≥ 0) and order M (with -L ≤ M ≤ L).
z
are the values for which to evaluate the polynomial. z
must satisfy -1≤ z ≤ +1 and can be a scalar or an array.
The optional input CSphase
(true
or false
) specifies whether the Condon-Shortley phase (-1)M should be included (true
) or not (false
). The default is true
.
plegendre
uses recurrence relations to compute the values, as described e.g. in Press et al, Numerical Recipes in C++ (2002).
clebschgordan, spherharm, wigner3j, wigner6j, wignerd