Formula:KLS:14.11:24

<< Formula:KLS:14.11:23

formula in Big q-Laguerre

Formula:KLS:14.11:25 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{a\rightarrow 0}\frac{P_{n}\!\left(aqx;a,ab;q\right)}{a^{n}}=q^{n}U^{(b)}_{n}\!\left(x;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqLaguerre
${\displaystyle{\displaystyle{\displaystyle U^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz I polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzI

Bibliography

Equation in Section 14.11 of KLS.

URL links

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formula in Big q-Laguerre

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