q-factorials

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1: 5.18 $q$-Gamma and $q$-Beta Functions

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§5.18(i) $q$-Factorials

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5.18.2 $$n{!}_q=1(1+q)\mathrm{\cdots }(1+q+\mathrm{\cdots }+q^{n-1})={(q;q)}_n{(1-q)}^{-n}.$$

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Defines:

${!}_q$: $q$-factorial (as in $n{!}_q$)

Symbols:

${(a;q)}_n$: $q$-Pochhammer symbol (or $q$-shifted factorial), $q$: real or complex variable and $n$: nonnegative integer

Permalink:

http://dlmf.nist.gov/5.18.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §5.18(i), §5.18 and Ch.5

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5.18.6 $$n{!}_q={\mathrm{\Gamma }}_q\left(n+1\right),$$

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Symbols:

${\mathrm{\Gamma }}_q\left(z\right)$: $q$-gamma function, ${!}_q$: $q$-factorial (as in $n{!}_q$), $q$: real or complex variable and $n$: nonnegative integer

Permalink:

http://dlmf.nist.gov/5.18.E6

Encodings:

pMML, png, TeX

See also:

Annotations for §5.18(ii), §5.18 and Ch.5

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