In mathematics, Bender–Dunne polynomials are a two-parameter family of sequences of orthogonal polynomials studied by Carl M. Bender and Gerald V. Dunne. ^{[1] [2]} They may be defined by the recursion:

${\displaystyle P_{0}(x)=1}$,

${\displaystyle P_{1}(x)=x}$ ,

and for ${\displaystyle n>1}$:

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

where ${\displaystyle J}$ and ${\displaystyle s}$ are arbitrary parameters.

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