Formula:KLS:14.29:03

<< Formula:KLS:14.29:02

formula in Discrete q-Hermite II

Formula:KLS:14.29:04 >>

${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}\!\left(x;q\right)=x^{n}\qHyperrphis{2}{1}@@{q^{-n},q^{-n+1}}{0}{q^{2}}{-\frac{q^{2}}{x^{2}}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}}}}$ : discrete ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite II polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteII
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.29 of KLS.

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<< Formula:KLS:14.29:02

formula in Discrete q-Hermite II

Formula:KLS:14.29:04 >>