Formula:6043

Digital Library of Mathematical Functions ID 17.3.E6

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

Symbols List

• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle E_{\NVar{q}}\left(\NVar{x}\right)}}$: $$q$$ -exponential function
• ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle q}}$: complex base
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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