Formula:KLS:14.16:12

{\displaystyle{\displaystyle{\displaystyle K^{\mathrm{Aff}}_{n}\!\left(q^{-x-1% };p,N;q\right)-K^{\mathrm{Aff}}_{n}\!\left(q^{-x};p,N;q\right){}=\frac{q^{-n-x% }(1-q^{n})}{(1-pq)(1-q^{-N})}K^{\mathrm{Aff}}_{n-1}\!\left(q^{-x};pq,N-1;q% \right)}}}

Proof

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