Formula:KLS:14.06:08

<< Formula:KLS:14.06:07

formula in q-Hahn

Formula:KLS:14.06:09 >>

${\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(q^{-x};\alpha,\beta,N;q\right)=\frac{\left(\alpha\beta q^{n+1};q\right)_{n}}{\left(\alpha q,q^{-N};q\right)_{n}}{\widehat{Q}}_{n}\!\left(q^{-x}\right){q}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle Q_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:qHahn
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{\widehat{Q}}_{n}}}}$ : monic ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:monicqHahn

Bibliography

Equation in Section 14.6 of KLS.

URL links

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<< Formula:KLS:14.06:07

formula in q-Hahn

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