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( q - N t ; q ) N - x \qHyperrphis 11 @ @ q - x p q q p q t = n = 0 N ( q - N ; q ) n ( q ; q ) n K n Aff ( q - x ; p , N ; q ) t n q-Pochhammer-symbol superscript 𝑞 𝑁 𝑡 𝑞 𝑁 𝑥 \qHyperrphis 11 @ @ superscript 𝑞 𝑥 𝑝 𝑞 𝑞 𝑝 𝑞 𝑡 superscript subscript 𝑛 0 𝑁 q-Pochhammer-symbol superscript 𝑞 𝑁 𝑞 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑛 affine-q-Krawtchouk-polynomial-K 𝑛 superscript 𝑞 𝑥 𝑝 𝑁 𝑞 superscript 𝑡 𝑛 {\displaystyle{\displaystyle{\displaystyle\left(q^{-N}t;q\right)_{N-x}\cdot% \qHyperrphis{1}{1}@@{q^{-x}}{pq}{q}{pqt}=\sum_{n=0}^{N}\frac{\left(q^{-N};q% \right)_{n}}{\left(q;q\right)_{n}}K^{\mathrm{Aff}}_{n}\!\left(q^{-x};p,N;q% \right)t^{n}}}}


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Symbols List

( a ; q ) n subscript 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}  : q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -Pochhammer symbol :
Σ Σ {\displaystyle{\displaystyle{\displaystyle\Sigma}}}  : sum :
K n Aff subscript superscript 𝐾 Aff 𝑛 {\displaystyle{\displaystyle{\displaystyle K^{\mathrm{Aff}}_{n}}}}  : affine q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -Krawtchouk polynomial :


Equation in Section 14.16 of KLS.

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