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)=xP_{n-1}(x)+16(n-1)(n-J-1)(n+2s-2)P_{n-2}(x)

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

References

Bender, Carl M.; Dunne, Gerald V. (1988), "Polynomials and operator orderings", Journal of Mathematical Physics, 29 (8): 1727–1731, doi:10.1063/1.527869, ISSN 0022-2488, MR 955168
Bender, Carl M.; Dunne, Gerald V. (1996), "Quasi-exactly solvable systems and orthogonal polynomials", Journal of Mathematical Physics, 37 (1): 6–11, doi:10.1063/1.531373, ISSN 0022-2488, MR 1370155

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