Delta sine

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Time Scale Sine Functions
$\mathbb{T}$
$\mathbb{R}$ $\sin_p(t,s)= $
$\mathbb{Z}$ $\sin_p(t,s) = \dfrac{\displaystyle\prod_{k=t_0}^{t-1}1+ip(k) - \displaystyle\prod_{k=t_0}^{t-1}1-ip(k)}{2i}$
$h\mathbb{Z}$ $\sin_p(t,s) = $
$\mathbb{Z}^2$ $\sin_p(t,s) = $
$\overline{q^{\mathbb{Z}}}, q > 1$ $\sin_p(t,s) = $
$\overline{q^{\mathbb{Z}}}, q < 1$ $\sin_p(t,s) =$
$\mathbb{H}$ $\sin_p(t,s) = $