Formula:KLS:01.09:10

<< Formula:KLS:01.09:09

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

Formula:KLS:01.09:11 >>

${\displaystyle{\displaystyle{\displaystyle\frac{1}{\left(q;q\right)_{n}}=\sum_{k=0}^{n}\frac{q^{k}}{\left(q;q\right)_{k}}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle n=0,1,2,\ldots}}}$

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
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum

Bibliography

Equation in Section 1.9 of KLS.

URL links

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<< Formula:KLS:01.09:09

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

Formula:KLS:01.09:11 >>