Formula:KLS:14.05:71

<< Formula:KLS:14.05:70

formula in Big q-Jacobi: Special case

Formula:KLS:14.05:72 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqLegendre
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-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 ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:monicbigqLegendre

Bibliography

Equation in Section 14.5 of KLS.

URL links

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<< Formula:KLS:14.05:70

formula in Big q-Jacobi: Special case

Formula:KLS:14.05:72 >>