Formula:KLS:14.12:40

<< Formula:KLS:14.12:36

formula in Little q-Jacobi: Special case

Formula:KLS:14.12:41 >>

${\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x|q\right)=\frac{q^{\binomial{n}{2}}(1-q)^{n}}{\left(q;q\right)_{n}}\left(\mathcal{D}_{q^{-1}}\right)^{n}\left[\left(qx;q\right)_{n}x^{n}\right]}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLegendre
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.12 of KLS.

URL links

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<< Formula:KLS:14.12:36

formula in Little q-Jacobi: Special case

Formula:KLS:14.12:41 >>