Formula:KLS:14.20:14

<< Formula:KLS:14.20:13

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:16 >>

${\displaystyle{\displaystyle{\displaystyle\mathcal{D}_{q^{-1}}\left[w(x;\alpha|q)p_{n}\!\left(x;q^{\alpha};q\right)\right]{}=\frac{1-q^{\alpha}}{q^{\alpha-1}(1-q)}w(x;\alpha-1|q)p_{n+1}\!\left(x;q^{\alpha-1};q\right)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle w(x;\alpha|q)=\left(qx;q\right)_{\infty}x^{\alpha}}}}$

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

Bibliography

Equation in Section 14.20 of KLS.

URL links

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<< Formula:KLS:14.20:13

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:16 >>