Difference between revisions of "Delta cosine"
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Revision as of 06:10, 1 March 2015
Let $\mathbb{T}$ be a time scale and let $t_0 \in \mathbb{T}$ and let $p \colon \mathbb{T} \rightarrow \mathbb{R}$ be a regressive function. We define the trigonometric functions $\cos_p \colon \mathbb{T} \rightarrow \mathbb{R}$ $$\cos_p(t,t_0)=\dfrac{e_{ip}(t,t_0)+e_{-ip}(t,t_0)}{2},$$ where $i=\sqrt{-1}$.
| $\mathbb{T}$ | |
| $\mathbb{R}$ | $\cos_p(t,s)= $ |
| $\mathbb{Z}$ | $\cos_p(t,s) = $ |
| $h\mathbb{Z}$ | $\cos_p(t,s) = $ |
| $\mathbb{Z}^2$ | $\cos_p(t,s) = $ |
| $\overline{q^{\mathbb{Z}}}, q > 1$ | $\cos_p(t,s) = $ |
| $\overline{q^{\mathbb{Z}}}, q < 1$ | $\cos_p(t,s) =$ |
| $\mathbb{H}$ | $\cos_p(t,s) = $ |
