Formula:KLS:14.14:03

{\displaystyle{\displaystyle{\displaystyle-pq^{2n+1}(1-q^{-x})K^{\mathrm{qtm}}% _{n}\!\left(q^{-x}\right){}=(1-q^{n-N})K^{\mathrm{qtm}}_{n+1}\!\left(q^{-x}% \right){}-\left[(1-q^{n-N})+q(1-q^{n})(1-pq^{n})\right]K^{\mathrm{qtm}}_{n}\!% \left(q^{-x}\right){}+q(1-q^{n})(1-pq^{n})K^{\mathrm{qtm}}_{n-1}\!\left(q^{-x}% \right)}}}

Proof

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