Formula:KLS:14.24:16

<< Formula:KLS:14.24:15

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:17 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{N\rightarrow\infty}K_{n}\!\left(\lambda(x);a^{-1},N|q\right)=\left(-\frac{1}{a}\right)^{n}q^{-\binomial{n}{2}}U^{(a)}_{n}\!\left(q^{x};q\right)}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$ : dual ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:dualqKrawtchouk
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle U^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz I polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzI

Bibliography

Equation in Section 14.24 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.24:15

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:17 >>