Difference between revisions of "Table:Delta hk"
From timescalewiki
| Line 3: | Line 3: | ||
|- | |- | ||
|$\mathbb{T}=$ | |$\mathbb{T}=$ | ||
| − | |$h_k(t,s)=$ | + | |$h_k(t,s;\mathbb{T})=$ |
|- | |- | ||
|[[Real_numbers | $\mathbb{R}$]] | |[[Real_numbers | $\mathbb{R}$]] | ||
Latest revision as of 01:31, 24 September 2016
| $\mathbb{T}=$ | $h_k(t,s;\mathbb{T})=$ |
| $\mathbb{R}$ | $\dfrac{(t-s)^k}{k!}$ |
| $\mathbb{Z}$ | $\displaystyle{t-s \choose k} = \dfrac{(t-s)!}{k! (t-s-k)!}$ |
| $h\mathbb{Z}$ | $\dfrac{1}{k!} \displaystyle\prod_{\ell=0}^{k-1}(t-\ell h-s)$ |
| $\mathbb{Z}^2$ | |
| $\overline{q^{\mathbb{Z}}}, q > 1$ | $\displaystyle\prod_{n=0}^{k-1} \dfrac{t-q^ns}{\sum_{i=0}^n q^i}$ |
| $\overline{q^{\mathbb{Z}}}, q < 1$ | |
| $\mathbb{H}$ |
