DLMF:17.3.E5 (Q5345)

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Language	Label	Description	Also known as
English	DLMF:17.3.E5	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}(-1)% ^{n}x^{2n}}{\left(q;q\right)_{2n}},}}

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DLMF:17.3.E5

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Symbols defined

$$q$$ -cosine function

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Defining formula

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

C1.S9.E1.m2abdec

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Defining formula

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

C17.S2.SS1.p1.m2addec

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$$q$$ -exponential function

Defining formula

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

C17.S3.E1.m2abdec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1ddec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1ddec

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Defining formula

{\displaystyle{\displaystyle x}}

C17.S1.XMD8.m1ddec

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