Formula:KLS:14.28:02

<< Formula:KLS:14.28:01

formula in Discrete q-Hermite I

Formula:KLS:14.28:03 >>

${\displaystyle{\displaystyle{\displaystyle h_{n}\!\left(x;q\right)=q^{\binomial{n}{2}}\,\qHyperrphis{2}{1}@@{q^{-n},x^{-1}}{0}{q}{-qx}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle h_{n}}}}$ : discrete ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite I polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteI
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.28 of KLS.

URL links

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<< Formula:KLS:14.28:01

formula in Discrete q-Hermite I

Formula:KLS:14.28:03 >>