# Delta cosine

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Let $\mathbb{T}$ be a time scale, let $t_0 \in \mathbb{T}$, and let $\mu p^2 \colon \mathbb{T} \rightarrow \mathbb{R}$ 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 $i=\sqrt{-1}$.

# Examples

 $\mathbb{T}$ $\cos_p(t,s)=$ $\mathbb{R}$ $\mathbb{Z}$ $h\mathbb{Z}$ $\mathbb{Z}^2$ $\overline{q^{\mathbb{Z}}}, q > 1$ $\overline{q^{\mathbb{Z}}}, q < 1$ $\mathbb{H}$

# See Also

 $\Delta$-special functions on time scales $\cos_p$ $\cosh_p$ $e_p$ $g_k$ $h_k$ $\sin_p$ $\sinh_p$