Bender–Dunne polynomials

In mathematics, Bender–Dunne polynomials are a two-parameter family of sequences of orthogonal polynomials studied by Carl M. Bender and Gerald V. Dunne. They may be defined by the recursion:


 * $$P_0(x) = 1$$,
 * $$P_{1}(x) = x$$ ,

and for $$n > 1$$:


 * $$P_n(x) = x P_{n-1}(x) + 16 (n-1) (n-J-1) (n + 2 s -2) P_{n-2}(x)$$

where $$J$$ and $$s$$ are arbitrary parameters.