An extended class of orthogonal polynomials defined by a Sturm???Liouville problem, Journal of Mathematical Analysis and Applications, vol.359, issue.1, p.352, 2009. ,
DOI : 10.1016/j.jmaa.2009.05.052
An extension of Bochner???s problem: Exceptional invariant subspaces, Journal of Approximation Theory, vol.162, issue.5, pp.987-1006, 2010. ,
DOI : 10.1016/j.jat.2009.11.002
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
On orthogonal polynomials spanning a non-standard flag, Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemporary Mathematics, 2012. ,
DOI : 10.1090/conm/563/11164
Two-step Darboux transformations and exceptional Laguerre polynomials, Journal of Mathematical Analysis and Applications, vol.387, issue.1, pp.410-418, 2012. ,
DOI : 10.1016/j.jmaa.2011.09.014
A Conjecture on Exceptional Orthogonal Polynomials, Foundations of Computational Mathematics, vol.9, issue.3, pp.615-666, 2013. ,
DOI : 10.1007/s10208-012-9128-6
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
Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics, Symmetry, Integrability and Geometry: Methods and Applications, issue.5, p.84, 2009. ,
DOI : 10.3842/SIGMA.2009.084
URL : http://doi.org/10.3842/sigma.2009.084
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, pp.337-347, 2009. ,
DOI : 10.1007/s12043-009-0126-4
An update on the \cal PT-symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally extended supersymmetric partners, Journal of Physics A: Mathematical and Theoretical, vol.43, issue.30, p.305301, 2010. ,
DOI : 10.1088/1751-8113/43/30/305301
Infinitely many shape invariant potentials and new orthogonal polynomials, Physics Letters B, vol.679, issue.4, pp.414-417, 2009. ,
DOI : 10.1016/j.physletb.2009.08.004
URL : http://doi.org/10.1016/j.physletb.2009.08.004
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, pp.173-176, 2010. ,
DOI : 10.1016/j.physletb.2009.12.062
) 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
Infinitely many shape-invariant potentials and cubic identities of the Laguerre and Jacobi polynomials, Journal of Mathematical Physics, vol.38, issue.5, p.53513, 2010. ,
DOI : 10.1016/j.physletb.2009.10.078
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
URL : http://arxiv.org/abs/1004.4711
Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials, Physics Letters B, vol.702, issue.2-3, pp.164-170, 2011. ,
DOI : 10.1016/j.physletb.2011.06.075
Krein???Adler transformations for shape-invariant potentials and pseudo virtual states, Journal of Physics A: Mathematical and Theoretical, vol.46, issue.24, p.245201, 2013. ,
DOI : 10.1088/1751-8113/46/24/245201
URL : http://arxiv.org/abs/1212.6595
Extensions of solvable potentials with finitely many discrete eigenstates, Journal of Physics A: Mathematical and Theoretical, vol.46, issue.23, p.235205, 2013. ,
DOI : 10.1088/1751-8113/46/23/235205
Conditionally exactly solvable potentials and exceptional orthogonal polynomials, Journal of Mathematical Physics, vol.5, issue.4, p.42101, 2010. ,
DOI : 10.1088/0305-4470/24/16/024
Zeros of the Exceptional Laguerre and Jacobi Polynomials, ISRN Mathematical Physics, vol.98, issue.107, p.107, 2011. ,
DOI : 10.1063/1.3651222
Confluence of apparent singularities in multi-indexed orthogonal polynomials: the Jacobi case, Journal of Physics A: Mathematical and Theoretical, vol.46, issue.11, p.115205, 2013. ,
DOI : 10.1088/1751-8113/46/11/115205
Solvable rational extension of translationally shape invariant potentials, " in Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemporary Mathematics, vol.563, 2012. ,
Solvable rational extensions of the isotonic oscillator, Annals of Physics, vol.326, issue.8, pp.2074-2090, 2011. ,
DOI : 10.1016/j.aop.2011.03.001
URL : https://hal.archives-ouvertes.fr/hal-00549822
Solvable rational extensions of the Morse and Kepler-Coulomb potentials, Journal of Mathematical Physics, vol.5, issue.10, p.103505, 2011. ,
DOI : 10.1088/0305-4470/32/7/019
URL : https://hal.archives-ouvertes.fr/hal-00579161
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
Rational solutions for the Riccati???Schr??dinger equations associated to translationally shape invariant potentials, Annals of Physics, vol.325, issue.6, pp.1235-1259, 2010. ,
DOI : 10.1016/j.aop.2010.03.008
New rational extensions of solvable potentials with finite bound state spectrum, Physics Letters A, vol.376, issue.45, pp.2866-2872, 2012. ,
DOI : 10.1016/j.physleta.2012.09.037
URL : https://hal.archives-ouvertes.fr/hal-00680522
Disconjugacy, regularity of multi-indexed rationally extended potentials, and Laguerre exceptional polynomials, Journal of Mathematical Physics, vol.1, issue.7, p.73512, 2013. ,
DOI : 10.1093/qmath/6.1.121
URL : https://hal.archives-ouvertes.fr/hal-00755966
Comments on the generalized SUSY QM partnership for Darboux???P??schl???Teller potential and exceptional Jacobi polynomials, Journal of Engineering Mathematics, vol.27, issue.1, pp.161-171, 2013. ,
DOI : 10.1007/s10665-012-9601-x
On the new translational shape-invariant potentials, Journal of Physics A: Mathematical and Theoretical, vol.44, issue.34, p.342001, 2011. ,
DOI : 10.1088/1751-8113/44/34/342001
Symmetries and the compatibility condition for the new translational shape invariant potentials, Physics Letters A, vol.376, issue.46, pp.3499-3503, 2012. ,
DOI : 10.1016/j.physleta.2012.10.033
Extended Krein-Adler theorem for the translationally shape invariant potentials, Journal of Mathematical Physics, vol.113, issue.4, p.43510, 2014. ,
DOI : 10.1088/0305-4470/32/7/019
URL : https://hal.archives-ouvertes.fr/hal-01513418
Supersymmetry, shape invariance, and exactly solvable potentials, American Journal of Physics, vol.56, issue.2, pp.163-168, 1988. ,
DOI : 10.1119/1.15697
Derivation of exact spectra of the Schrodinger equation by means of supersymmetry, JETP Lett, vol.38, pp.356-359, 1983. ,
Supersymmetric quantum mechanics of one-dimensional systems, Journal of Physics A: Mathematical and General, vol.18, issue.15, pp.2917-2936, 1985. ,
DOI : 10.1088/0305-4470/18/15/020
Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials, Journal of Physics A: Mathematical and Theoretical, vol.47, issue.1, p.15203, 2014. ,
DOI : 10.1088/1751-8113/47/1/015203
Ordinary Differential Equations, 1964. ,
The theory of disconjugacy for a second order linear differential equations ,
HIGHER-ORDER SUSY, EXACTLY SOLVABLE POTENTIALS, AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS, Modern Physics Letters A, vol.5, issue.25, pp.1843-1852, 2011. ,
DOI : 10.1016/j.aop.2009.08.002
RATIONALLY-EXTENDED RADIAL OSCILLATORS AND LAGUERRE EXCEPTIONAL ORTHOGONAL POLYNOMIALS IN kTH-ORDER SUSYQM, International Journal of Modern Physics A, vol.7, issue.32, pp.5337-5347, 2011. ,
DOI : 10.1063/1.530209
Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials, Symmetry, Integrability and Geometry: Methods and Applications, vol.8, p.80, 2012. ,
DOI : 10.3842/SIGMA.2012.080
REVISITING (QUASI-)EXACTLY SOLVABLE RATIONAL EXTENSIONS OF THE MORSE POTENTIAL, International Journal of Modern Physics A, vol.7, issue.13, p.1250073, 2012. ,
DOI : 10.1016/j.aop.2009.08.002
INTEGRABILITY OF THE RICCATI EQUATION FROM A GROUP-THEORETICAL VIEWPOINT, International Journal of Modern Physics A, vol.24, issue.12, pp.1935-1951, 1999. ,
DOI : 10.1142/S0217751X98002298
Group Theoretical Approach to the Intertwined Hamiltonians, Annals of Physics, vol.292, issue.1, pp.42-66, 2001. ,
DOI : 10.1006/aphy.2001.6179
On a continuous analogue of a Christoffel formula from the theory of orthogonal polynomials, Dokl. Akad. Nauk SSSR, vol.113, p.970, 1957. ,
A modification of Crum's method, Theoretical and Mathematical Physics, vol.23, issue.2, pp.1381-1386, 1994. ,
DOI : 10.1007/BF01035458
Supersymmetry, factorisation of the Schrodinger equation and a Hamiltonian hierarchy, Journal of Physics A: Mathematical and General, vol.18, issue.2, pp.57-61, 1985. ,
DOI : 10.1088/0305-4470/18/2/001
The factorization method and quantum systems with equivalent energy spectra, Physics Letters A, vol.105, issue.1-2, pp.19-22, 1984. ,
DOI : 10.1016/0375-9601(84)90553-X
Higher-derivative supersymmetry and the Witten index, Physics Letters A, vol.174, issue.4, pp.273-279, 1993. ,
DOI : 10.1016/0375-9601(93)90137-O
Darboux transformation, factorization, and supersymmetry in one-dimensional quantum mechanics, Theoretical and Mathematical Physics, vol.102, issue.5, pp.1051-1060, 1995. ,
DOI : 10.1007/BF02065985
Darboux transformation and elementary exact solutions of the Schr??dinger equation, Pramana, vol.27, issue.6, pp.563-580, 1997. ,
DOI : 10.1007/BF02848330
Darboux transformation and exactly solvable potentials with quasi-equidistant spectrum, Russian Physics Journal, vol.102, issue.3, pp.765-771, 1995. ,
DOI : 10.1007/BF00559274
N-order Darboux transformation and a spectral problem on semiaxis ,
New possibilities for supersymmetry breakdown in quantum mechanics and second-order irreducible Darboux transformations, Physics Letters A, vol.263, issue.4-6, pp.274-280, 1999. ,
DOI : 10.1016/S0375-9601(99)00736-7
URL : http://arxiv.org/abs/quant-ph/9904009
A simple generation of exactly solvable anharmonic oscillators, Physics Letters A, vol.244, issue.5, pp.309-316, 1998. ,
DOI : 10.1016/S0375-9601(98)00298-9
Second-order supersymmetric periodic potentials, Physics Letters A, vol.275, issue.5-6, pp.338-349, 2000. ,
DOI : 10.1016/S0375-9601(00)00591-0
Second order SUSY transformations with ???complex energies???, Physics Letters A, vol.308, issue.1, pp.11-16, 2003. ,
DOI : 10.1016/S0375-9601(02)01779-6
The finite difference algorithm for higher order supersymmetry, Physics Letters A, vol.269, issue.2-3, pp.70-78, 2000. ,
DOI : 10.1016/S0375-9601(00)00226-7
URL : http://arxiv.org/abs/quant-ph/0004024
Monodromy-free Schr??dinger operators with quadratically increasing potentials, Theoretical and Mathematical Physics, vol.6, issue.3, pp.1574-1584, 1999. ,
DOI : 10.1007/BF02557204
Differential equations in the spectral parameter, Communications in Mathematical Physics, vol.4, issue.4, pp.177-240, 1986. ,
DOI : 10.1007/BF01206937
Darboux transformations for multidimensional Schr??dinger operators, Russian Mathematical Surveys, vol.53, issue.2, pp.377-379, 1998. ,
DOI : 10.1070/RM1998v053n02ABEH000033
On the singularities of potentials of exactly soluble Schr??dinger equations and on Hadamard's problem, Russian Mathematical Surveys, vol.53, issue.1, pp.208-209, 1998. ,
DOI : 10.1070/RM1998v053n01ABEH000022
Equidistant spectra of anharmonic oscillators, pp.47-53, 1994. ,
Supersymmetric method for constructing quasi-exactly and conditionally-exactly solvable potentials, Journal of Physics A: Mathematical and General, vol.32, issue.7, pp.1291-1312, 1999. ,
DOI : 10.1088/0305-4470/32/7/019
URL : http://arxiv.org/abs/quant-ph/9808050
Special Functions, 2000. ,