  Weak gravitational, electromagnetic, neutrino and scalar fields, considered
as perturbations on Kerr background satisfy Teukolsky Master Equation. The two
non-trivial equations obtained after separating the variables are the polar
angle equation and the radial equation. We solve them by transforming each one
into the form of a confluent Heun equation. The transformation depends on a set
of parameters, which can be chosen in a such a way, so the resulting equations
have simple polynomial solutions for neutrino, electromagnetic, and
gravitational perturbations, provided some additional conditions are satisfied.
Remarkably there exists a class of solutions for which these additional
conditions are the same for the two different equations for $|s|=1/2$ and
$|s|=1$. As a result the additional conditions fix the dependence of the
separation constant on the angular frequency but the frequency itself remains
unconstrained and belongs to a continuous spectrum.
