Formula:KLS:14.24:11

<< Formula:KLS:14.24:10

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:13 >>

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

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle w(x;a;q)=\left(qx,a^{-1}qx;q\right)_{\infty}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle U^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz I polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzI
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.24 of KLS.

URL links

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<< Formula:KLS:14.24:10

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:13 >>