Overlapping of Lévai’s and Milson’s E-Tangent-Polynomial Potentials along Symmetric Curves

Comment: To make the presentation more consistent with the journal style. I re-formulated the most important result of the paper as Theorem 4.1 while turning the main body of Section 4 into its proof.  The theorem was also formulated as a new advance in the theory of solvable rational Sturm-Liouville equations rather than a certain development in its quantum-mechanical applications dealing solely with the Liouville form of these equations. The theorem 4.1 was then re-stated again as a corollary dealing solely with the Liouville form of the JRef and RRef CSLEs.I found it useful to incorporate Theorem 3.1 at the introductory part of Section 3 which relates the square integrability of eigenfunctions of the Schrödinger equation on the line to the Dirichlet problem for the prime SLE.  Similar statements were also added to Introduction to shift the focus from the quantum mechanical theory of solvable potentials to the theory of RCSLEs with quasi-rational eigenfunctions. I included an example illustrating Theorem 4.1 for the Rosen-Morse and Gendenshtein potentials overlapping along the symmetric sech-squared curves. In addition to Discussion I also added Conclusions which summarizes the current analysis in a more general context.Finally I carefully traced all the spelling Editor marks.