A new family of shape invariantly deformed Darboux-Pöschl-Teller potentials with continuous \ell

Abstract: 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 theconditionally exactly solvable potentials' on a half line.