Formula:KLS:14.25:17

<< Formula:KLS:14.25:16

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:18 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{N\rightarrow\infty}K^{\mathrm{qtm}}_{n}\!\left(x;a^{-1}q^{-N-1},N;q\right)=\left(-\frac{1}{a}\right)^{n}q^{\binomial{n}{2}}V^{(a)}_{n}\!\left(x;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{qtm}}_{n}}}}$ : quantum ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:qtmqKrawtchouk
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle V^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz II polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzII

Bibliography

Equation in Section 14.25 of KLS.

URL links

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<< Formula:KLS:14.25:16

formula in Al-Salam-Carlitz II

Formula:KLS:14.25:18 >>