Formula:KLS:14.28:18

<< Formula:KLS:14.28:17

formula in Discrete q-Hermite I

Formula:KLS:14.28:19 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}\frac{h_{n}\!\left(x\sqrt{1-q^{2}};q\right)}{(1-q^{2})^{\frac{n}{2}}}=\frac{H_{n}\left(x\right)}{2^{n}}}}}$

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
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : Hermite polynomial ${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : http://dlmf.nist.gov/18.3#T1.t1.r28

Bibliography

Equation in Section 14.28 of KLS.

URL links

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<< Formula:KLS:14.28:17

formula in Discrete q-Hermite I

Formula:KLS:14.28:19 >>