Formula:KLS:14.18:29

<< Formula:KLS:14.18:28

formula in Continuous big q-Hermite

Formula:KLS:14.19:01 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : continuous big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsbigqHermite
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : Hermite polynomial ${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : http://dlmf.nist.gov/18.3#T1.t1.r28

Bibliography

Equation in Section 14.18 of KLS.

URL links

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formula in Continuous big q-Hermite

Formula:KLS:14.19:01 >>