Formula:KLS:01.10:11

<< Formula:KLS:01.10:10

formula in Basic hypergeometric functions

Formula:KLS:01.11:01 >>

${\displaystyle{\displaystyle{\displaystyle Q_{N}\!\left(q^{-x};\alpha,\beta,N;q\right)=\sum_{k=0}^{N}\frac{\left(\alpha\beta q^{N+1};q\right)_{k}\left(q^{-x};q\right)_{k}}{\left(\alpha q;q\right)_{k}\left(q;q\right)_{k}}q^{k}}}}$

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

Bibliography

Equation in Section 1.10 of KLS.

URL links

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<< Formula:KLS:01.10:10

formula in Basic hypergeometric functions

Formula:KLS:01.11:01 >>