Formula:KLS:14.24:19

<< Formula:KLS:14.24:18

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:20 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle U^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz I polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzI
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : Hermite polynomial ${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : http://dlmf.nist.gov/18.3#T1.t1.r28

Bibliography

Equation in Section 14.24 of KLS.

URL links

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<< Formula:KLS:14.24:18

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:20 >>