Formula:KLS:14.05:24

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formula in Big q-Jacobi

Formula:KLS:14.05:25 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{c\rightarrow-\infty}P_{n}\!\left(cqx;a,b,c;q\right)=p_{n}\!\left(x;a,b;q\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi

Bibliography

Equation in Section 14.5 of KLS.

URL links

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formula in Big q-Jacobi

Formula:KLS:14.05:25 >>