Formula:KLS:14.29:24

<< Formula:KLS:14.29:23

formula in Discrete q-Hermite II

Formula:KLS:14.29:25 >>

${\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(1;a,b;q\right)=(-a)^{n}q^{\frac{1}{2}n(n+1)}\frac{\left(qb;q\right)_{n}}{\left(qa;q\right)_{n}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.29 of KLS.

URL links

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<< Formula:KLS:14.29:23

formula in Discrete q-Hermite II

Formula:KLS:14.29:25 >>