Formula:KLS:14.14:18

<< Formula:KLS:14.14:17

formula in Quantum q-Krawtchouk

Formula:KLS:14.14:19 >>

${\displaystyle{\displaystyle{\displaystyle\left(q^{x-N}t;q\right)_{N-x}\cdot\qHyperrphis{2}{1}@@{q^{-x},pq^{N+1-x}}{0}{q}{q^{x-N}t}{}=\sum_{n=0}^{N}\frac{\left(q^{-N};q\right)_{n}}{\left(q;q\right)_{n}}K^{\mathrm{qtm}}_{n}\!\left(q^{-x};p,N;q\right)t^{n}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{qtm}}_{n}}}}$ : quantum ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:qtmqKrawtchouk

Bibliography

Equation in Section 14.14 of KLS.

URL links

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formula in Quantum q-Krawtchouk

Formula:KLS:14.14:19 >>