  The tridiagonal representation approach is an algebraic method for solving
second order differential wave equations. Using this approach in the solution
of quantum mechanical problems, we encounter two new classes of orthogonal
polynomials whose properties give the structure and dynamics of the
corresponding physical system. For a certain range of parameters, one of these
polynomials has a mix of continuous and discrete spectra making it suitable for
describing physical systems with both scattering and bound states. In this
work, we define these polynomials by their recursion relations and highlight
some of their properties using numerical means. Due to the prime significance
of these polynomials in physics, we hope that our short expose will encourage
experts in the field of orthogonal polynomials to study them and derive their
properties (weight functions, generating functions, asymptotics, orthogonality
relations, zeros, etc.) analytically.
