Bender–Dunne polynomials

In mathematics, Bender–Dunne polynomials are a two-parameter family of sequences of orthogonal polynomials studied by Bender and Dunne (1988, 1996). 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.

References

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