New formulas for the eigenfunctions of the two-particle difference Calogero-Moser system (Q839594)

The differential equation \[ -y''+\left(\frac{m(m+1)\alpha^2}{\cos^2\alpha x}+\frac{n(n+1)\alpha^2}{\sin^2\alpha x}\right)y=\lambda y \] is known as Darboux-Pöschl-Teller (DPT) equation. The authors present a new proof of the integrability of a functional-difference deformation of DPT equation which is denoted by DDPT. The proof is based on some formula for special Casorati determinants established in the article. The obtained formula provides some new representation for the DDPT potentials as well as for the general solution.