Formula:KLS:14.20:02

<< Formula:KLS:14.20:01

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:03 >>

${\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x;a;q\right)=\frac{1}{\left(a^{-1}q^{-n};q\right)_{n}}\,\qHyperrphis{2}{0}@@{q^{-n},x^{-1}}{-}{q}{\frac{x}{a}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre / Wall polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLaguerre
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.20 of KLS.

URL links

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<< Formula:KLS:14.20:01

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:03 >>