An approach to one-dimensional elliptic quasi-exactly solvable models

One-dimensional Jacobian elliptic quasi-exactly solvable second-order differential equations are obtained by introducing the generalized third master functions. It is shown that the solutions of these differential equations are generating functions for a new set of polynomials in terms of energy with factorization property. The roots of these polynomials are the same as the eigenvalues of the differential equations. Some one-dimensional elliptic quasi-exactly quantum solvable models are obtained from these differential equations.