associated Legendre functions could be found from Legendre functions according to the following formula
so in MATLAB you can define a function like this
function plm = assocLegendre(l,m)
% get symbolic associated legendre function P_lm(x) based on
% legendre function P_l(x)
syms x;
% get symbolic form of Legendre function P_l(x)
leg = legendreP(l,x);
% differentiate it m times
legDiff = diff(leg,x,m);
% calculate associated legendre function P_lm(x)
plm = ((-1)^m)*((1 - x^2)^(m/2))*legDiff;
end
to get associated Legendre functions in symbolic form.
