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• Delta exponential
  ...et $p \in \mathcal{R}(\mathbb{T},\mathbb{C})$ be a [[regressive_function | regressive function]]. The $\Delta$-exponential function $e_p (\cdot,\cdot;\mathbb{T}) $$e_p(t,s;\mathbb{T}) = \exp \left( \displaystyle\int_s^t \xi_{\mu(\tau)}(p(\tau))\Delta \tau \right),$$
  4 KB (689 words) - 14:12, 28 January 2023
• Forward regressive
  ...t $p \colon \mathbb{T} \rightarrow \mathbb{C}$. We say that $p$ is forward regressive if for all $t \in \mathbb{T}^{\kappa}$ $$1+\mu(t)p(t)\neq 0.$$
  253 bytes (42 words) - 12:58, 16 January 2023
• Abel's theorem
  ...$ and assume $y^{\Delta \Delta}(t) + p(t) y^{\Delta}(t) + q(t)y(t) = 0$ is regressive, where $p$ and $q$ are [[rd continuous]]. Suppose that $y_1$ and $y_2$ are $$W(t) = e_{-p+\mu q}(t,t_0)W(t_0)$$
  464 bytes (77 words) - 12:48, 16 January 2023
• Delta simple useful formula
  ...b{T}$, and $p \in \mathcal{R} \left( \mathbb{T},\mathbb{C} \right)$ be a [[regressive function]]. The following formula holds: $$e_p(\sigma(t),s;\mathbb{T})=(1+\mu(t)p(t))e_p(t,s;\mathbb{T}),$$
  645 bytes (97 words) - 06:08, 10 June 2016
• Exponential distribution
  ...0$ and $\ominus \lambda$ be [[positively mu regressive | positively $\mu$-regressive]] constant functions and let $t \in \mathbb{T}$. The exponential distributi
  644 bytes (81 words) - 14:07, 28 January 2023
• Delta cosh
  Let $p \in C_{rd}$ and $-\mu p^2$ be a [[regressive function]]. Then the $\Delta$-hyperbolic cosine function is defined by
  1 KB (169 words) - 14:13, 28 January 2023
• Delta sinh
  Let $p$ and $-\mu p^2$ be [[regressive function|regressive functions]]. Then the $\Delta$ hyperbolic sine function is defined by
  611 bytes (86 words) - 14:13, 28 January 2023
• Delta sine
  ...p^2 \colon \mathbb{T} \rightarrow \mathbb{R}$ be a [[regressive_function | regressive function]]. We define the trigonometric function $\sin_p \colon \mathbb{T}
  826 bytes (124 words) - 14:13, 28 January 2023
• Delta cosine
  ...p^2 \colon \mathbb{T} \rightarrow \mathbb{R}$ be a [[regressive_function | regressive function]]. We define the trigonometric functions $\cos_p \colon \mathbb{T}
  877 bytes (127 words) - 14:13, 28 January 2023
• Relationship between delta exponential and nabla exponential
  If $q$ is [[continuous]] and [[mu regressive | $\mu$-regressive]] then
  392 bytes (58 words) - 22:22, 9 June 2016
• Forward circle minus
  ...cal{R}(\mathbb{T},\mathbb{C})$ be [[forward regressive function| (forward) regressive functions ]]. We define the (forward) circle minus operation by $$\left( \ominus_{\mu} p \right)(t) = \dfrac{-p(t)}{1+p(t)\mu(t)}.$$
  523 bytes (77 words) - 15:26, 21 January 2023
• Forward positively regressive
  ...mathbb{T} \rightarrow \mathbb{C}$. We say that $p$ is (forward) positively regressive if for all $t \in \mathbb{T}^{\kappa}$ $$1+\mu(t)p(t) > 0.$$
  287 bytes (44 words) - 12:57, 16 January 2023