Gómez-Ullate Oteiza, DavidGrandati, YvesMilson, Robert2023-06-162023-06-162020-050021-904510.1016/j.jat.2019.105350https://hdl.handle.net/20.500.14352/6203© 2019 Published by Elsevier Inc. We would like to thank Antonio Duran for bringing this observation to our attention and taking part in rigorous discussions on the matter. We would like to thank Paul Nevai for motivating this exchange with Antonio Duran and giving us the opportunity to prepare this amended proof. The research of DGU has been supported in part by Spanish MINECO, Spain FEDER Grants RTI2018-100754-B-I00 and PGC2018-096504-B-C33. The research of RM was supported in part by Natural Sciences and Engineering Research Council, Canada grant RGPIN-228057-2009.Exceptional orthogonal polynomials are complete families of orthogonal polynomials that arise as eigenfunctions of a Sturm-Liouville problem. Antonio Duran discovered a gap in the original proof of completeness for exceptional Hermite polynomials, that has propagated to analogous results for other exceptional families In this paper we provide an alternative proof that follows essentially the same arguments, but provides a direct proof of the key lemma on which the completeness proof is based. This direct proof makes use of the theory of trivial monodromy potentials developed by Duistermaat and Grtinbaum and Oblomkov. (C) 2019 Published by Elsevier Inc.engAtribución-NoComercial-SinDerivadas 3.0 Españahttps://creativecommons.org/licenses/by-nc-nd/3.0/es/journal articlehttp://dx.doi.org/10.1016/j.jat.2019.105350https://www.sciencedirect.com/open access51-73Exceptional Hermite polynomialsTrivial monodromy potentialsCompleteness.Física-Modelos matemáticosFísica matemática