Generalized master function approach to one-dimensional quasiexactly solvable models (Q2738280)

By introducing the generalized master function of order up to four together with corresponding weight functions, we have obtained all one-dimensional quasiexactly solvable second order differential equations. It is shown that these differential equations have solutions of polynomial type with factorization properties, that is polynomial solutions \(P_m(E)\) can be factorized in terms of polynomials \(P_{n+1}(E)\) for \(m\geq n+1\). All known one-dimensional quasiexactly quantum solvable models can be obtained from these differential equations, where the roots of the polynomials \(P_{n+1}(E)\) are the corresponding eigenvalues.