Delta cosh

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Time Scale $\Delta$-$\cosh_1$ Functions
$\mathbb{T}=$ $\cosh_1(t,0)=$
$\mathbb{R}$ $\cosh_1(t,0)=\cosh(t)$
$\mathbb{Z}$
$h\mathbb{Z}$ $\cosh_1(t,0)=\dfrac{1}{2}\left( (1-h)^{\frac{t}{h}} + (1+h)^{\frac{t}{h}} \right)$
$\mathbb{Z}^2$
$\overline{q^{\mathbb{Z}}}, q > 1$
$\overline{q^{\mathbb{Z}}}, q < 1$
$\mathbb{H}$