DLMF:17.3.E6 (Q5346)

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DLMF:17.3.E6
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    Defining formula
    Cos q ⁡ ( x ) = 1 2 ⁢ ( E q ⁡ ( i ⁢ x ) + E q ⁡ ( - i ⁢ x ) ) = ∑ n = 0 ∞ ( 1 - q ) 2 ⁢ n ⁢ q n ⁢ ( 2 ⁢ n - 1 ) ⁢ ( - 1 ) n ⁢ x 2 ⁢ n ( q ; q ) 2 ⁢ n . q-Cos 𝑞 𝑥 1 2 q-Exp 𝑞 𝑖 𝑥 q-Exp 𝑞 𝑖 𝑥 superscript subscript 𝑛 0 superscript 1 𝑞 2 𝑛 superscript 𝑞 𝑛 2 𝑛 1 superscript 1 𝑛 superscript 𝑥 2 𝑛 q-Pochhammer-symbol 𝑞 𝑞 2 𝑛 {\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 id
    DLMF:17.3.E6
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