Formula:KLS:14.11:02

<< Formula:KLS:14.11:01

formula in Big q-Laguerre

Formula:KLS:14.11:03 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqLaguerre
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-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 14.11 of KLS.

URL links

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<< Formula:KLS:14.11:01

formula in Big q-Laguerre

Formula:KLS:14.11:03 >>