We show how to separate variables in the problem of three anyons with
a harmonic oscillator potential. The anyonic symmetry conditions from
cyclic permutations are separable in our coordinates. The conditions f
rom two-particle transpositions are not separable, but can be expresse
d as reflection symmetry conditions on the wave function and its norma
l derivative on the boundary of a circle. We solve this one-dimensiona
l problem numerically by discretization.