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on 27 Oct 2021
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N=4;
L=3;
M=1;
r=meshgrid(0:.5:50);
t=r'/25*pi;
a=N-L-1;
% Short version of laguerre polynomial
F=0;
for i=0:a
F=F+(-1)^i*nchoosek(N+L,a-i)*(2*r/N).^i/prod(1:i);
end
G=legendre(L,cos(t));
P=squeeze(G(1+M,:,:)).*F.*exp(-r/2).*r.^L;
contourf(r.*sin(t),r.*cos(t),abs(P),1e3,'edgec','n');
caxis([0 5]);
axis equal off;
axis(35*[-1 1 -1 1]);
colormap hot;
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