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 $n>1$:

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

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

References

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