DLMF:17.3.E6 (Q5346)

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Language	Label	Description	Also known as
English	DLMF:17.3.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathrm{Cos}_{q}\left(x\right)=\frac{1}{2}(E_{q}% \left(ix\right)+E_{q}\left(-ix\right))=\sum_{n=0}^{\infty}\frac{(1-q)^{2n}q^{n% (2n-1)}(-1)^{n}x^{2n}}{\left(q;q\right)_{2n}}.}}

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DLMF:17.3.E6

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Symbols defined

$$q$$ -cosine function

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2acdec

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$$q$$ -exponential function

Defining formula

{\displaystyle{\displaystyle E_{\NVar{q}}\left(\NVar{x}\right)}}

C17.S3.E2.m2abdec

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

C17.S2.SS1.p1.m2aedec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1edec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1edec

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Defining formula

{\displaystyle{\displaystyle x}}

C17.S1.XMD8.m1edec

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Sitelinks

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