"Rotation operator part 1" Y(l,m) = (-1)^m sqrt((2 l + 1) / (4 pi) (l - m)! / (l + m)!) * P(l,m) exp(i m phi) -- associated Legendre of cos theta (arxiv.org/abs/1805.12125) P(l,m,k) = test(m < 0, (-1)^m (l + m)! / (l - m)! P(l,-m), (sin(theta)/2)^m sum(k, 0, l - m, (-1)^k (l + m + k)! / (l - m - k)! / (m + k)! / k! * ((1 - cos(theta)) / 2)^k)) psi = Y(3,2) + Y(3,1) + Y(3,0) "Verify equation (1)" R(f,a) = f + a d(f,phi) + 1/2 a^2 d(f,phi,2) + 1/6 a^3 d(f,phi,3) Rpsi = eval(psi, phi, phi + a) check(R(psi,a) == taylor(Rpsi, a, 3, 0)) "ok" "Verify equation (2)" R(f,a) = f + a d(f,theta) + 1/2 a^2 d(f,theta,2) + 1/6 a^3 d(f,theta,3) Rpsi = eval(psi, theta, theta + a) check(R(psi,a) == taylor(Rpsi, a, 3, 0)) "ok" Run