Formula:KLS:14.21:06

{\displaystyle{\displaystyle{\displaystyle-q^{2n+\alpha+1}xL^{(\alpha)}_{n}\!% \left(x;q\right)=(1-q^{n+1})L^{(\alpha)}_{n+1}\!\left(x;q\right){}-\left[(1-q^% {n+1})+q(1-q^{n+\alpha})\right]L^{(\alpha)}_{n}\!\left(x;q\right){}+q(1-q^{n+% \alpha})L^{(\alpha)}_{n-1}\!\left(x;q\right)}}}

Proof

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