Table:Delta hk

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Time Scale $h_k$ Monomials
$\mathbb{T}=$ $h_k(t,s;\mathbb{T})=$
$\mathbb{R}$ $\dfrac{(t-s)^k}{k!}$
$\mathbb{Z}$ $\displaystyle{t-s \choose k} = \dfrac{(t-s)!}{k! (t-s-k)!}$
$h\mathbb{Z}$ $\dfrac{1}{k!} \displaystyle\prod_{\ell=0}^{k-1}(t-\ell h-s)$
$\mathbb{Z}^2$
$\overline{q^{\mathbb{Z}}}, q > 1$ $\displaystyle\prod_{n=0}^{k-1} \dfrac{t-q^ns}{\sum_{i=0}^n q^i}$
$\overline{q^{\mathbb{Z}}}, q < 1$
$\mathbb{H}$