# q-sine function

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## 4 matching pages

##### 1: 17.3 $q$-Elementary and $q$-Special Functions
###### $q$-SineFunctions
17.3.3 $\operatorname{sin}_{q}\left(x\right)=\frac{1}{2i}(e_{q}\left(ix\right)-e_{q}% \left(-ix\right))=\sum_{n=0}^{\infty}\frac{(1-q)^{2n+1}(-1)^{n}x^{2n+1}}{\left% (q;q\right)_{2n+1}},$
17.3.4 $\operatorname{Sin}_{q}\left(x\right)=\frac{1}{2i}(E_{q}\left(ix\right)-E_{q}% \left(-ix\right))=\sum_{n=0}^{\infty}\frac{(1-q)^{2n+1}q^{n(2n+1)}(-1)^{n}x^{2% n+1}}{\left(q;q\right)_{2n+1}}.$
##### 2: 28.4 Fourier Series
28.4.3 $\operatorname{se}_{2n+1}\left(z,q\right)=\sum_{m=0}^{\infty}B^{2n+1}_{2m+1}(q)% \sin(2m+1)z,$
28.4.4 $\operatorname{se}_{2n+2}\left(z,q\right)=\sum_{m=0}^{\infty}B^{2n+2}_{2m+2}(q)% \sin(2m+2)z.$
##### 3: 28.6 Expansions for Small $q$
28.6.23 $\operatorname{se}_{1}\left(z,q\right)=\sin z-\tfrac{1}{8}q\sin 3z+\tfrac{1}{12% 8}q^{2}\left(\tfrac{2}{3}\sin 5z+2\sin 3z-\sin z\right)-\tfrac{1}{1024}q^{3}% \left(\tfrac{1}{9}\sin 7z+\tfrac{8}{9}\sin 5z-\tfrac{1}{3}\sin 3z-2\sin z% \right)+\cdots,$
28.6.25 $\operatorname{se}_{2}\left(z,q\right)=\sin 2z-\tfrac{1}{12}q\sin 4z+\tfrac{1}{% 128}q^{2}\left(\tfrac{1}{3}\sin 6z-\tfrac{4}{9}\sin 2z\right)+\cdots.$
##### 4: 28.14 Fourier Series
28.14.3 $\operatorname{se}_{\nu}\left(z,q\right)=\sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(% q)\sin(\nu+2m)z,$