  Supersymmetric quantum mechanics has many applications, and typically uses a
raising and lowering operator formalism. For one dimensional problems, we show
how such raising and lowering operators may be generalized to include an
arbitrary function. As a result, the usual Rodrigues' formula of the theory of
orthogonal polynomials may be recovered in special cases, and it may otherwise
be generalized to incorporate an arbitrary function. We provide example
generalized operators for several important classical orthogonal polynomials,
including Chebyshev, Gegenbauer, and other polynomials. In particular, as
concerns Legendre polynomials and associated Legendre functions, we supplement
and generalize results of Bazeia and Das.
