Formula:KLS:14.05:27

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formula in Big q-Jacobi

Formula:KLS:14.05:28 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}P_{n}\!\left(x;q^{\alpha},q^{\beta},-q^{\gamma};q\right)=\frac{P^{(\alpha,\beta)}_{n}\left(x\right)}{P^{(\alpha,\beta)}_{n}\left(1\right)}}}}$

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
${\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}$ : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3

Bibliography

Equation in Section 14.5 of KLS.

URL links

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formula in Big q-Jacobi

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