Formula:KLS:14.13:20

<< Formula:KLS:14.13:19

formula in q-Meixner

Formula:KLS:14.13:21 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{c\rightarrow-\infty}P_{n}\!\left(q^{-x};a,-a^{-1}cd^{-1},c;q\right)=M_{n}\!\left(q^{-x};a,d;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqJacobi
${\displaystyle{\displaystyle{\displaystyle M_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Meixner polynomial : http://drmf.wmflabs.org/wiki/Definition:qMeixner

Bibliography

Equation in Section 14.13 of KLS.

URL links

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<< Formula:KLS:14.13:19

formula in q-Meixner

Formula:KLS:14.13:21 >>