In three dimensions, the spherical harmonic differential equation is given by [1/(sin θ) d/(dθ)(sin θd/(dθ)) + 1/(sin^2 θ) d^2/(dϕ^2) + l(l + 1)] u = 0, and solutions are called spherical harmonics. In four dimensions, the spherical harmonic differential equation is u_(x x) + 2u_x cot x + csc^2 x(u_(y y) + u_y cot y + u_(z z) csc^2 y) + (n^2 - 1) u = 0 (Humi 1987; Zwillinger 1997, p. 130).
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