Difference between revisions of "Delta gk"
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(Created page with "==$g_k$ polynomials== $$g_0(t,s)=1$$ $$g_{n}(t,s) = \displaystyle\int_s^t g_{n-1}(\sigma(\tau),s) \Delta \tau$$ {| class="wikitable" |+Time Scale $g_k$ Monomials |- |$\mathbb...") |
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$$g_{n}(t,s) = \displaystyle\int_s^t g_{n-1}(\sigma(\tau),s) \Delta \tau$$ | $$g_{n}(t,s) = \displaystyle\int_s^t g_{n-1}(\sigma(\tau),s) \Delta \tau$$ | ||
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Revision as of 07:56, 23 March 2015
$g_k$ polynomials
$$g_0(t,s)=1$$ $$g_{n}(t,s) = \displaystyle\int_s^t g_{n-1}(\sigma(\tau),s) \Delta \tau$$
| $\mathbb{T}=$ | $g_k(t,t_0)=$ |
| $\mathbb{R}$ | $g_k(t,t_0)=\dfrac{(t-t_0)^k}{k!}$ |
| $\mathbb{Z}$ | $g_k(t,t_0)= $ |
| $h\mathbb{Z}$ | $g_k(t,t_0)=$ |
| $\mathbb{Z}^2$ | $g_k(t,t_0)=$ |
| $\overline{q^{\mathbb{Z}}}, q > 1$ | $g_k(t,t_0)=$ |
| $\overline{q^{\mathbb{Z}}}, q < 1$ | $g_k(t,t_0)=$ |
| $\mathbb{H}$ | $g_k(t,t_0)=$ |
