Formula:KLS:14.08:31

<< Formula:KLS:14.08:30

formula in Al-Salam-Chihara

Formula:KLS:14.08:32 >>

${\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(x;q^{\frac{1}{2}\alpha+\frac{1}{4}},q^{\frac{1}{2}\alpha+\frac{3}{4}}\,|\,q\right)=\frac{\left(q;q\right)_{n}}{q^{(\frac{1}{2}\alpha+\frac{1}{4})n}}P^{(\alpha)}_{n}\!\left(x|q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle Q_{n}}}}$ : Al-Salam-Chihara polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamChihara
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle P^{(n)}_{\alpha}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqLaguerre

Bibliography

Equation in Section 14.8 of KLS.

URL links

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<< Formula:KLS:14.08:30

formula in Al-Salam-Chihara

Formula:KLS:14.08:32 >>