Difference between revisions of "Delta cosh"
From timescalewiki
(Created page with "{| class="wikitable" |+Time Scale $\Delta$-$\cosh_1$ Functions |- |$\mathbb{T}=$ |$\cosh_1(t,0)=$ |- | $\mathbb{R}$ | $\cosh_1(t,0)=\cosh(t)$ |- |Integers ...") |
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|[[Multiples_of_integers | $h\mathbb{Z}$]] | |[[Multiples_of_integers | $h\mathbb{Z}$]] | ||
| − | | $\cosh_1(t,0)=\dfrac{1}{2}\left( (1-h)^{\frac{t}{h}} + (1+h)^{\frac{t}{h}} \right)$ | + | | $\cosh_1(t,0)=\dfrac{1}{2}\left( (1-h)^{\frac{t}{h}} + (1+h)^{\frac{t}{h}} = \displaystyle\sum_{k=0}^{\infty} h_{2k}(t,0) \right)$ |
|- | |- | ||
| [[Square_integers | $\mathbb{Z}^2$]] | | [[Square_integers | $\mathbb{Z}^2$]] | ||
Revision as of 19:49, 28 February 2015
| $\mathbb{T}=$ | $\cosh_1(t,0)=$ |
| $\mathbb{R}$ | $\cosh_1(t,0)=\cosh(t)$ |
| $\mathbb{Z}$ | |
| $h\mathbb{Z}$ | $\cosh_1(t,0)=\dfrac{1}{2}\left( (1-h)^{\frac{t}{h}} + (1+h)^{\frac{t}{h}} = \displaystyle\sum_{k=0}^{\infty} h_{2k}(t,0) \right)$ |
| $\mathbb{Z}^2$ | |
| $\overline{q^{\mathbb{Z}}}, q > 1$ | |
| $\overline{q^{\mathbb{Z}}}, q < 1$ | |
| $\mathbb{H}$ |
