Formula:KLS:14.12:22

<< Formula:KLS:14.12:21

formula in Little q-Jacobi

Formula:KLS:14.12:23 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{b\rightarrow-\infty}p_{n}\!\left(-b^{-1}q^{-1}x;q^{\alpha},b;q\right)=\frac{\left(q;q\right)_{n}}{\left(q^{\alpha+1};q\right)_{n}}L^{(\alpha)}_{n}\!\left(x;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:qLaguerre

Bibliography

Equation in Section 14.12 of KLS.

URL links

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<< Formula:KLS:14.12:21

formula in Little q-Jacobi

Formula:KLS:14.12:23 >>