Gómez-Ullate Otaiza, DavidKamran, N.Milson, R.2023-06-202023-06-202010-10-291751-8113https://hdl.handle.net/20.500.14352/44630© IOP Publishing Ltd. The research of DGU was supported in part by MICINN-FEDER grant MTM2009- 06973 and CUR-DIUE grant 2009SGR859. The research of NK was supported in part by NSERC grant RGPIN 105490-2004. The research of RM was supported in part by NSERC grant RGPIN-228057-2004.We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described X(m) Laguerre polynomials in terms of an isospectral Darboux transformation. We also show that the shape invariance of these new polynomial families is a direct consequence of the permutability property of the Darboux-Crum transformation.engjournal articlehttp://dx.doi.org/10.1088/1751-8113/43/43/434016http://iopscience.iop.orghttp://arxiv.org/abs/1002.2666open access51-73Shape-invariant potentialsQuasi-exact solvabilityQuantum-mechanicsSupersymmetrySystemsFísica-Modelos matemáticosFísica matemática