Formula:KLS:14.05:63

<< Formula:KLS:14.05:62

formula in Big q-Jacobi

Formula:KLS:14.05:64 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{a\to\infty}{\mathrm{i}^{n}}q^{\frac{1}{2}n(n-1)}P_{n}\!\left(q^{-1}a^{-1}\mathrm{i}x;a,a,1,1;q\right)=\tilde{h}_{n}\!\left(x;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial with four parameters : http://drmf.wmflabs.org/wiki/Definition:bigqJacobiIVparam
${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}}}}$ : discrete ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite II polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteII

Bibliography

Equation in Section 14.5 of KLS.

URL links

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<< Formula:KLS:14.05:62

formula in Big q-Jacobi

Formula:KLS:14.05:64 >>