We present a new family of shape invariant potentials which could be called a ``continuous \ell version" of the potentials corresponding to the exceptional (X_{ \ell}) J1 Jacobi polynomials constructed recently by the present authors. In a certain limit, it reduces to a continuous \ell family of shape invariant potentials related to the exceptional (X_{ \ell}) L1 Laguerre polynomials. The latter was known as one example of the `conditionally exactly solvable potentials' on a half line.
Categories: math-ph hep-th math.CA math.MP nlin.SI quant-ph