-- Y returns a spherical harmonic eigenfunction Y(l,m) = (-1)^m sqrt((2l + 1)/(4pi) (l - m)!/(l + m)!) * P(expcos(theta),l,m) exp(i m phi) -- P returns an associated Lengendre function P(f,n,m) = eval(1/(2^n n!) (1 - x^2)^(m/2) * d((x^2 - 1)^n,x,n + m),x,f) "Eigenfunctions" Y(0,0) Y(1,0) Y(1,1) Y(1,-1) Y(2,0) Y(2,1) Y(2,2) Y(2,-1) Y(2,-2) "Verify (1=ok)" S(l,m) = -Lap(Y(l,m)) == l (l + 1) Y(l,m) Lap(f) = 1/expsin(theta) d(expsin(theta) d(f,theta),theta) + 1/expsin(theta)^2 d(f,phi,2) S(0,0) S(1,0) S(1,1) S(1,-1) S(2,0) S(2,1) S(2,2) S(2,-1) S(2,-2)

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