Multiples of integers

The set $h\mathbb{Z}=\{\ldots,-2h,-h,0,h,2h,\ldots\}$ of multiples of the integers is a time scale.

$\mathbb{T}=h\mathbb{Z}$

Generic element $t\in \mathbb{T}$:	For some $n \in \mathbb{Z}, t =hn$
Jump operator:	$\sigma(t)=t+h$
Graininess operator:	$\mu(t)=h$
$\Delta$-derivative:	$f^{\Delta}(t)=\dfrac{f(t+h)-f(t)}{h}$
$\Delta$-integral:	$\displaystyle\int_s^t f(\tau) \Delta \tau = \displaystyle\sum_{k=\frac{s}{h}}^{\frac{t}{h}-1} hf(hk)$
Exponential function:	$\begin{array}{ll} e_p(t,s) &= \exp \left( \displaystyle\int_{s}^{t} \dfrac{1}{\mu(\tau)} \log(1 + hp(\tau)) \Delta \tau \right) \\ &= \exp \left( \displaystyle\sum_{k=\frac{s}{h}}^{\frac{t}{h}-1} \log(1+hp(hk)) \right) \\ &= \displaystyle\prod_{k=\frac{s}{h}}^{\frac{t}{h}-1} \left( 1+hp(hk) \right) \\ \end{array}$