D. Gómez-ullate, N. Kamran, and R. Milson, The Darboux transformation and algebraic deformations of shape-invariant potentials, " e-print arXiv:quant-ph/0308062

D. Gómez-ullate, N. Kamran, and R. Milson, Supersymmetry and algebraic Darboux transformations, Journal of Physics A: Mathematical and General, vol.37, issue.43, p.10065, 2004.
DOI : 10.1088/0305-4470/37/43/004

D. Gómez-ullate, N. Kamran, and R. Milson, An extended class of orthogonal polynomials defined by a Sturm-Liouville problem, " e-print arXiv:0807.3939, J. Math. Anal

D. Gómez-ullate, N. Kamran, and R. Milson, An extension of Bochner???s problem: Exceptional invariant subspaces, Journal of Approximation Theory, vol.162, issue.5, p.987, 2010.
DOI : 10.1016/j.jat.2009.11.002

C. Quesne, Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.39, p.392001, 2008.
DOI : 10.1088/1751-8113/41/39/392001

URL : http://arxiv.org/abs/0807.4087

L. E. Gendenshtein, Derivation of exact spectra of the Schrödinger equation by means of supersymmetry, JETP Lett, vol.38, p.356, 1983.

F. Cooper, A. Khare, and U. Sukhatme, Supersymmetry and quantum mechanics, Physics Reports, vol.251, issue.5-6, p.267, 1995.
DOI : 10.1016/0370-1573(94)00080-M

J. F. Cariñena and A. Ramos, parameters transformed by translation, Journal of Physics A: Mathematical and General, vol.33, issue.17, p.3467, 2000.
DOI : 10.1088/0305-4470/33/17/305

B. Bagchi, C. Quesne, and R. Roychoudhury, Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBqj3BWbIqubWexLMBb50ujbqegm0B % 1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr % Ffpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0F % irpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaa % GcbaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYtUvgaiuaacqWF % pepucqWFtepvaaa!46A4! $$ \mathcal{P}\mathcal{T} $$ symmetry, Pramana, vol.19, issue.2, p.337, 2009.
DOI : 10.1007/s12043-009-0126-4

C. Quesne, Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics, Symmetry, Integrability and Geometry: Methods and Applications, p.84, 2009.
DOI : 10.3842/SIGMA.2009.084

S. Odake and R. Sasaki, Infinitely many shape invariant potentials and new orthogonal polynomials, Physics Letters B, vol.679, issue.4, p.414, 2009.
DOI : 10.1016/j.physletb.2009.08.004

URL : http://doi.org/10.1016/j.physletb.2009.08.004

S. Odake and R. Sasaki, Another set of infinitely many exceptional <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>???</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math> Laguerre polynomials, Physics Letters B, vol.684, issue.2-3, p.173, 2010.
DOI : 10.1016/j.physletb.2009.12.062

S. Odake and R. Sasaki, Infinitely many shape-invariant potentials and cubic identities of the Laguerre and Jacobi polynomials, Journal of Mathematical Physics, vol.51, issue.5, p.53513, 2010.
DOI : 10.1063/1.3371248

C. Ho, S. Odake, and R. Sasaki, ) Laguerre and Jacobi Polynomials, Symmetry, Integrability and Geometry: Methods and Applications, vol.7, p.107, 2011.
DOI : 10.3842/SIGMA.2011.107

URL : http://doi.org/10.5402/2012/920475

R. Sasaki, S. Tsujimoto, and A. Zhedanov, Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux???Crum transformations, Journal of Physics A: Mathematical and Theoretical, vol.43, issue.31, p.315204, 2010.
DOI : 10.1088/1751-8113/43/31/315204

D. Gómez-ullate, N. Kamran, and R. Milson, Exceptional orthogonal polynomials and the Darboux transformation, Journal of Physics A: Mathematical and Theoretical, vol.43, issue.43, p.434016, 2010.
DOI : 10.1088/1751-8113/43/43/434016

D. Gómez-ullate, N. Kamran, and R. Milson, On orthogonal polynomials spanning a non-standard flag, Contemp. Math, vol.563, p.51, 2012.
DOI : 10.1090/conm/563/11164

Y. Grandati, Solvable rational extensions of the isotonic oscillator, Annals of Physics, vol.326, issue.8, p.2074, 2011.
DOI : 10.1016/j.aop.2011.03.001

URL : https://hal.archives-ouvertes.fr/hal-00549822

C. Ho, Prepotential Approach to Solvable Rational Potentials and Exceptional Orthogonal Polynomials, Progress of Theoretical Physics, vol.126, issue.2, p.185, 2011.
DOI : 10.1143/PTP.126.185

URL : http://arxiv.org/abs/1104.3511

S. Yu, V. M. Dubov, N. E. Eleonskii, and . Kulagin, Equidistant spectra of anharmonic oscillators, Sov. Phys. JETP, vol.75, p.446, 1992.

S. Yu, V. M. Dubov, N. E. Eleonskii, and . Kulagin, Equidistant spectra of anharmonic oscillators, p.47, 1994.

V. G. Bagrov and B. F. Samsonov, Darboux transformation, factorization, and supersymmetry in one-dimensional quantum mechanics, Theoretical and Mathematical Physics, vol.102, issue.5, p.1051, 1995.
DOI : 10.1007/BF02065985

B. F. Samsonov, New features in supersymmetry breakdown in quantum mechanics, " e-print arXiv:quant-ph/9611012; Mod, Phys. Lett. A, vol.11, p.1563, 1996.

G. Junker and P. Roy, Conditionally exactly solvable problems and non-linear algebras, Physics Letters A, vol.232, issue.3-4, p.155, 1997.
DOI : 10.1016/S0375-9601(97)00422-2

G. Junker and P. Roy, Conditionally Exactly Solvable Potentials: A Supersymmetric Construction Method, Annals of Physics, vol.270, issue.1, p.155, 1998.
DOI : 10.1006/aphy.1998.5856

URL : http://arxiv.org/abs/quant-ph/9803024

J. F. Cariñena, A. M. Perelomov, M. F. Rañada, and M. Santander, A quantum exactly solvable nonlinear oscillator related to the isotonic oscillator, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.8, p.85301, 2008.
DOI : 10.1088/1751-8113/41/8/085301

J. M. Fellows and R. A. Smith, Factorization solution of a family of quantum nonlinear oscillators, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.33, p.335303, 2009.
DOI : 10.1088/1751-8113/42/33/335303

D. Gómez-ullate, N. Kamran, and R. Milson, Two-step Darboux transformations and exceptional Laguerre polynomials, Journal of Mathematical Analysis and Applications, vol.387, issue.1, p.410, 2012.
DOI : 10.1016/j.jmaa.2011.09.014

S. Odake and R. Sasaki, Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials, Physics Letters B, vol.702, issue.2-3, p.164, 2011.
DOI : 10.1016/j.physletb.2011.06.075

C. Quesne, Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials, " e-print arXiv:1106.1990; Mod, Phys. Lett. A, vol.26, p.1843, 2011.

C. Quesne, RATIONALLY-EXTENDED RADIAL OSCILLATORS AND LAGUERRE EXCEPTIONAL ORTHOGONAL POLYNOMIALS IN kTH-ORDER SUSYQM, International Journal of Modern Physics A, vol.26, issue.32, p.5337, 2011.
DOI : 10.1142/S0217751X11054942

Y. Grandati, Multistep DBT and regular rational extensions of the isotonic oscillator, Annals of Physics, vol.327, issue.10, p.2411, 2012.
DOI : 10.1016/j.aop.2012.07.004

URL : https://hal.archives-ouvertes.fr/hal-00614879

D. Gómez-ullate, N. Kamran, and R. Milson, A Conjecture on Exceptional Orthogonal Polynomials, Foundations of Computational Mathematics, vol.9, issue.3
DOI : 10.1007/s10208-012-9128-6

G. Szegö, Orthogonal Polynomials (Amer, Math. Soc, 1939.

P. Hartman, Ordinary Differential Equations, 1964.

A. A. Andrianov, M. V. Ioffe, and V. Spiridonov, Higher-derivative supersymmetry and the Witten index, Physics Letters A, vol.174, issue.4, p.273, 1993.
DOI : 10.1016/0375-9601(93)90137-O

A. A. Andrianov, M. V. Ioffe, F. Cannata, and J. Dedonder, SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM, International Journal of Modern Physics A, vol.10, issue.18, p.2683, 1995.
DOI : 10.1142/S0217751X95001261

D. J. Fernández, C. , and N. Fernández-garcía, Higher-order supersymmetric quantum mechanics, " e-print arXiv:quant-ph, Proc. 744, p.236, 2005.

M. M. Crum, ASSOCIATED STURM-LIOUVILLE SYSTEMS, The Quarterly Journal of Mathematics, vol.6, issue.1, p.121, 1955.
DOI : 10.1093/qmath/6.1.121

T. Muir, A treatise on the theory of determinants, 1960.