  We consider the problem of three identical charged particles on a plane under
a perpendicular magnetic field and interacting through Coulomb repulsion. This
problem is treated within Taut's framework, in the limit of vanishing center of
mass vector $\vec{R} \to \vec{0}$, which corresponds to the strong magnetic
field limit, occuring for example in the Fractional Quantum Hall Effect. Using
the solutions of the biconfluent Heun equation, we compute the eigenstates and
show that there is two sets of solutions. The first one corresponds to a system
of three independent anyons which have their angular momenta fixed by the value
of the magnetic field and specified by a dimensionless parameter $C \simeq
\frac{l_B}{l_0}$, the ratio of $l_B$, the magnetic length, over $l_0$, the Bohr
radius. This anyonic character, consistent with quantum mechanics of identical
particles in two dimensions, is induced by competing physical forces. The
second one corresponds to the case of the Landau problem when $C \to 0$.
Finally we compare these states with the quantum Hall states and find that the
Laughlin wave functions are special cases of our solutions under certains
conditions.
