Formula:KLS:14.12:08

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formula in Little q-Jacobi

Formula:KLS:14.12:12 >>

${\displaystyle{\displaystyle{\displaystyle q^{-n}(1-q^{n})(1-abq^{n+1})xy(x){}=B(x)y(qx)-\left[B(x)+D(x)\right]y(x)+D(x)y(q^{-1}x)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle D(x)=x-1}}}$ &

${\displaystyle{\displaystyle{\displaystyle B(x)=a(bqx-1)}}}$ &

${\displaystyle{\displaystyle{\displaystyle y(x)=p_{n}\!\left(x;a,b;q\right)}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi

Bibliography

Equation in Section 14.12 of KLS.

URL links

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<< Formula:KLS:14.12:07

formula in Little q-Jacobi

Formula:KLS:14.12:12 >>