Formula:KLS:14.10:96

{\displaystyle{\displaystyle{\displaystyle x{\widehat{P}}_{n}\!\left(x\right)=% {\widehat{P}}_{n+1}\!\left(x\right)+\frac{(1-q^{n})^{2}}{4(1-q^{n-\frac{1}{2}}% )(1-q^{n+\frac{1}{2}})}{\widehat{P}}_{n-1}\!\left(x\right)}}}

Proof

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