Formula:KLS:14.07:08

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formula in Dual q-Hahn

Formula:KLS:14.07:09 >>

${\displaystyle{\displaystyle{\displaystyle x{\widehat{R}}_{n}\!\left(x\right)={\widehat{R}}_{n+1}\!\left(x\right)+\left[1+\gamma\delta q-(A_{n}+C_{n})\right]{\widehat{R}}_{n}\!\left(x\right){}+\gamma q(1-q^{n})(1-\gamma q^{n}){}(1-q^{n-N-1})(\delta-q^{n-N-1}){\widehat{R}}_{n-1}\!\left(x\right)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle C_{n}=\gamma q\left(1-q^{n}\right)\left(\delta-q^{n-N-1}\right)}}}$ &
${\displaystyle{\displaystyle{\displaystyle A_{n}=\left(1-q^{n-N}\right)\left(1-\gamma q^{n+1}\right)}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle{\widehat{R}}_{n}}}}$ : monic dual ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:monicdualqHahn

Bibliography

Equation in Section 14.7 of KLS.

URL links

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formula in Dual q-Hahn

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