Bender-Dunne Orthogonal Polynomials General Theory

A general theory of Bender-Dunne orthogonal polynomials is proposed. It is shown that these polynomials can easily be constructed for any explicitly tridiagonalizable Hamiltonians and are, in fact, the orthogonal polynomials in a discrete variable which takes its values in the set of energy levels of the corresponding quantum model. The weight functions for Bender-Dunne polynomials are explicitly constructed.