Formula:KLS:14.05:07

<< Formula:KLS:14.05:06

formula in Big q-Jacobi

Formula:KLS:14.05:08 >>

${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(x;a,b,c;q\right)=\frac{\left(abq^{n+1};q\right)_{n}}{\left(aq,cq;q\right)_{n}}{\widehat{P}}_{n}\!\left(x\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqJacobi
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}_{n}}}}$ : monic big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:monicbigqJacobi

Bibliography

Equation in Section 14.5 of KLS.

URL links

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<< Formula:KLS:14.05:06

formula in Big q-Jacobi

Formula:KLS:14.05:08 >>