Delta cosine

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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 $i=\sqrt{-1}$.


Derivative of delta cosine
Sum of squares of delta cosine and delta sine
Derivative of Delta sine


Time Scale Cosine Functions
$\mathbb{T}$ $\cos_p(t,s)= $
$\overline{q^{\mathbb{Z}}}, q > 1$
$\overline{q^{\mathbb{Z}}}, q < 1$

See Also[edit]

Delta sine
Delta cosh

$\Delta$-special functions on time scales