Formula:KLS:14.05:57

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formula in Big q-Jacobi

Formula:KLS:14.05:58 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{a\to 0}a^{-n}P_{n}\!\left(x;a,a,1,1;q\right)=q^{n}h_{n}\!\left(x;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial with four parameters : http://drmf.wmflabs.org/wiki/Definition:bigqJacobiIVparam
${\displaystyle{\displaystyle{\displaystyle h_{n}}}}$ : discrete ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite I polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteI

Bibliography

Equation in Section 14.5 of KLS.

URL links

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