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The paper applies the so-called 'Canonical-Darboux-Transformation' (CDT)method to reproduce general expressions for rational potentials (RPs) quantizedin terms of exceptional orthogonal polynomial systems (X-OPSs). The benchmarkof the new method recently developed by the author for implicit potentialssolvable via hypergeometric functions is that rationally-extended SUSY partnersof the original potential are quantized in terms of sequences of the so-called'Gauss-seed' (GS) Heine polynomials starting from a polynomial of non-zeroorder. The common mark of the Darboux-Poschl-Teller (DPT) potential andisotonic oscillator discussed in this paper is that the appropriate rationalSturm-Liouville (RSL) equations have energy-independent characteristicexponents at both singular end points and as a result the appropriate sequencesof GS Heine polynomials turn into X-OPSs with infinitely many members.

Gauss-Seed Nets of Sturm-Liouville Problems With Energy-Independent  Characteristic Exponents and Related Sequences of Exceptional Orthogonal  Polynomials I. Canonical Darboux Transformations Using AEH Functions