  The Schr\" odinger equations which are exactly solvable in terms of
associated special functions are directly related to some self-adjoint
operators defined in the theory of hypergeometric type equations. The
fundamental formulae occurring in a supersymmetric approach to these
Hamiltonians are consequences of some formulae concerning the general theory of
associated special functions. We use this connection in order to obtain a
general theory of Schr\" odinger equations exactly solvable in terms of
associated special functions, and to extend certain results known in the case
of some particular potentials.
