Formula:KLS:01.09:08

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formula in The q-gamma function and q-binomial coefficients

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${\displaystyle{\displaystyle{\displaystyle\frac{\left(q^{\alpha+1};q\right)_{n}}{\left(q;q\right)_{n}}=\genfrac{[}{]}{0.0pt}{}{n+\alpha}{n}_{q}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{0}{}{n}{j}_{q}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-binomial coefficient (or Gaussian polynomial) : http://dlmf.nist.gov/17.2#E27 http://dlmf.nist.gov/26.9#SS2.p1

Bibliography

Equation in Section 1.9 of KLS.

URL links

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formula in The q-gamma function and q-binomial coefficients

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