Delta gk

$g_k$ polynomials

$$g_0(t,s)=1$$ $$g_{n}(t,s) = \displaystyle\int_s^t g_{n-1}(\sigma(\tau),s) \Delta \tau$$

Delta $g_k$ Monomials

$\mathbb{T}=$	$g_k(t,t_0)=$
$\mathbb{R}$	$g_k(t,t_0)=\dfrac{(t-t_0)^k}{k!}$
$\mathbb{Z}$	$g_k(t,t_0)= $
$h\mathbb{Z}$	$g_k(t,t_0)=$
$\mathbb{Z}^2$	$g_k(t,t_0)=$
$\overline{q^{\mathbb{Z}}}, q > 1$	$g_k(t,t_0)=$
$\overline{q^{\mathbb{Z}}}, q < 1$	$g_k(t,t_0)=$
$\mathbb{H}$	$g_k(t,t_0)=$