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- 13:41, 20 January 2023 (diff | hist) . . (+54) . . Delta derivative of unilateral convolution
- 13:41, 20 January 2023 (diff | hist) . . (+287) . . N Delta derivative of unilateral convolution (Created page with "==Theorem== If $f$ is $\Delta$-differentiable, then $$(f*g)^{\Delta}=f^{\Delta}*g+f(t_0)g.$$ If $g$ is $\Delta$-differentiable, then...")
- 13:40, 20 January 2023 (diff | hist) . . (-337) . . Unilateral convolution
- 13:39, 20 January 2023 (diff | hist) . . (-13) . . Unilateral convolution
- 13:38, 20 January 2023 (diff | hist) . . (+142) . . N Unilateral convolution is associative (Created page with "==Theorem== Convolution is associative, i.e. $$(f*g)*h = f*(g*h).$$ ==Proof== ==References== Category:Theorem Category:Unproven")
- 13:37, 20 January 2023 (diff | hist) . . (+6) . . Unilateral convolution (→Properties)
- 13:37, 20 January 2023 (diff | hist) . . (-205) . . Unilateral convolution
- 13:37, 20 January 2023 (diff | hist) . . (+321) . . N Covolution theorem for unilateral Laplace transform (Created page with "==Theorem== The following formula holds: $$\widehat{(f*g)}(t,s)=\displaystyle\int_s^t \hat{f}(t,\sigma(\xi))\hat{g}(\xi,s) \Delta \xi,$$ where $\widehat{(f*g)}$ denotes the so...")
- 13:36, 20 January 2023 (diff | hist) . . (-1,053) . . Unilateral convolution
- 12:58, 16 January 2023 (diff | hist) . . (0) . . m Forward regressive (Tom moved page Forward regressive function to Forward regressive) (current)
- 12:58, 16 January 2023 (diff | hist) . . (+32) . . N Forward regressive function (Tom moved page Forward regressive function to Forward regressive) (current)
- 12:57, 16 January 2023 (diff | hist) . . (0) . . m Forward positively regressive (Tom moved page Forward positively regressive function to Forward positively regressive) (current)
- 12:57, 16 January 2023 (diff | hist) . . (+43) . . N Forward positively regressive function (Tom moved page Forward positively regressive function to Forward positively regressive) (current)
- 12:57, 16 January 2023 (diff | hist) . . (+23) . . Forward positively regressive
- 12:57, 16 January 2023 (diff | hist) . . (+264) . . N Forward positively regressive (Created page with "Let $\mathbb{T}$ be a time scale. Let $p \colon \mathbb{T} \rightarrow \mathbb{C}$. We say that $p$ is (forward) positively regressive if for all $t \in \math...")
- 12:56, 16 January 2023 (diff | hist) . . (+91) . . Delta Bernoulli inequality
- 12:53, 16 January 2023 (diff | hist) . . (+25) . . Bracket number (current)
- 12:53, 16 January 2023 (diff | hist) . . (+25) . . Bracket factorial (current)
- 12:53, 16 January 2023 (diff | hist) . . (+25) . . Gamma function (current)
- 12:53, 16 January 2023 (diff | hist) . . (+25) . . Bilateral Laplace transform
- 12:53, 16 January 2023 (diff | hist) . . (+25) . . Pre-differentiable (current)
- 12:53, 16 January 2023 (diff | hist) . . (-124) . . Forward regressive
- 12:50, 16 January 2023 (diff | hist) . . (+49) . . Bilateral Laplace transform
- 12:50, 16 January 2023 (diff | hist) . . (+10) . . Bilateral Laplace transform
- 12:48, 16 January 2023 (diff | hist) . . (+56) . . Abel's theorem (current)
- 12:46, 16 January 2023 (diff | hist) . . (-231) . . Abel's theorem
- 12:43, 16 January 2023 (diff | hist) . . (+14) . . Pre-differentiable
- 12:43, 16 January 2023 (diff | hist) . . (+6) . . Main Page
- 12:43, 16 January 2023 (diff | hist) . . (0) . . m First mean value theorem (Tom moved page Mean value theorem to First mean value theorem) (current)
- 12:43, 16 January 2023 (diff | hist) . . (+38) . . N Mean value theorem (Tom moved page Mean value theorem to First mean value theorem) (current)
- 12:42, 16 January 2023 (diff | hist) . . (-123) . . First mean value theorem
- 12:41, 16 January 2023 (diff | hist) . . (+8) . . Main Page (→Calculus on time scales)
- 02:35, 16 January 2023 (diff | hist) . . (+79) . . Main Page
- 02:33, 16 January 2023 (diff | hist) . . (+294) . . Paper:Tom Cuchta/Analysis of the bilateral Laplace transform on time scales with applications (current)
- 02:31, 16 January 2023 (diff | hist) . . (-7) . . Cuchta-Georgiev Fourier transform
- 02:31, 16 January 2023 (diff | hist) . . (+44) . . Bilateral Laplace transform
- 02:31, 16 January 2023 (diff | hist) . . (+50) . . Unilateral Laplace transform
- 02:31, 16 January 2023 (diff | hist) . . (+40) . . Bilateral Laplace transform
- 02:30, 16 January 2023 (diff | hist) . . (+161) . . Bilateral Laplace transform
- 18:09, 15 January 2023 (diff | hist) . . (+9) . . Gamma function (→Examples of gamma functions)
- 18:09, 15 January 2023 (diff | hist) . . (+19) . . Gamma function (→Examples of gamma functions)
- 18:08, 15 January 2023 (diff | hist) . . (+50) . . Forward box plus (current)
- 18:08, 15 January 2023 (diff | hist) . . (+50) . . Gamma function of x boxplus one (current)
- 18:08, 15 January 2023 (diff | hist) . . (+99) . . Bracket factorial
- 18:07, 15 January 2023 (diff | hist) . . (+99) . . Bracket number
- 18:07, 15 January 2023 (diff | hist) . . (+108) . . Gamma function on certain time scales at bracket number equals bracket factorial (current)
- 18:06, 15 January 2023 (diff | hist) . . (+11) . . Gamma function
- 18:06, 15 January 2023 (diff | hist) . . (0) . . m Gamma function on certain time scales at bracket number equals bracket factorial (Tom moved page Gamma function on integers at bracket number equals bracket factorial to Gamma function on certain time scales at bracket number equals bracket factorial)
- 18:06, 15 January 2023 (diff | hist) . . (+94) . . N Gamma function on integers at bracket number equals bracket factorial (Tom moved page Gamma function on integers at bracket number equals bracket factorial to Gamma function on certain time scales at bracket number equals bracket factorial) (current)
- 18:06, 15 January 2023 (diff | hist) . . (-120) . . Gamma function on certain time scales at bracket number equals bracket factorial
- 18:05, 15 January 2023 (diff | hist) . . (+506) . . N Gamma function on certain time scales at bracket number equals bracket factorial (Created page with "==Theorem== <div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $n \in \mathbb{Z}^+$ and assume that $[k]_{\mathbb{T}}$ is a...")
- 18:05, 15 January 2023 (diff | hist) . . (-346) . . Gamma function (→Properties of gamma functions)
- 18:04, 15 January 2023 (diff | hist) . . (0) . . m Bracket number (Tom moved page Bracket numbers to Bracket number)
- 18:04, 15 January 2023 (diff | hist) . . (+28) . . N Bracket numbers (Tom moved page Bracket numbers to Bracket number) (current)
- 18:03, 15 January 2023 (diff | hist) . . (+311) . . N Bracket factorial (Created page with "Let $\mathbb{T}$ be a time scale. Define the bracket factorial by $$[n]_{\mathbb{T}}! = \left\{ \begin{array}{ll} 1&; n=0 \\ \displaystyle\prod_{j=1}^n [j]_{\mathbb{T}} &;...")
- 18:03, 15 January 2023 (diff | hist) . . (-167) . . Gamma function (→Properties of gamma functions)
- 18:02, 15 January 2023 (diff | hist) . . (+19) . . Bracket number
- 18:02, 15 January 2023 (diff | hist) . . (+122) . . Bracket number
- 18:01, 15 January 2023 (diff | hist) . . (+199) . . N Bracket number (Created page with "Define the bracket number operators (they are actually functions) $$[n]_{\mathbb{T}} = \left\{ \begin{array}{ll} 0 &; n=0 \\ [n-1]_{\mathbb{T}} \boxplus_{\mu} 1 &; n=1,2,\ldo...")
- 18:01, 15 January 2023 (diff | hist) . . (-199) . . Gamma function (→Properties of gamma functions)
- 18:01, 15 January 2023 (diff | hist) . . (+11) . . Gamma function of x boxplus one
- 18:00, 15 January 2023 (diff | hist) . . (+326) . . N Gamma function of x boxplus one (Created page with "==Theorem== If $\mathbb{T}$ is a time scale and $s \in \mathbb{T}^+$, then for all $x \in \mathbb{R}^+$, $$\Gamma_{\mathbb{T}}(x \boxplus_{\mu} 1;s) = \dfrac{x}{s} \Gamma_...")
- 17:58, 15 January 2023 (diff | hist) . . (-285) . . Gamma function (→Properties of gamma functions)
- 17:57, 15 January 2023 (diff | hist) . . (+242) . . N Gamma function equals one at one (Created page with "==Theorem== If $\mathbb{T}$ is a time scale and $s \in \mathbb{T}^+$, then $$\Gamma_{\mathbb{T}}(1;s)=1,$$ where $\Gamma_{\mathbb{T}}$ denotes the gamma function. ==...") (current)
- 17:56, 15 January 2023 (diff | hist) . . (-198) . . Gamma function (→Properties of gamma functions)
- 17:56, 15 January 2023 (diff | hist) . . (+60) . . Gamma function diverges at infinity (current)
- 17:55, 15 January 2023 (diff | hist) . . (+230) . . N Gamma function diverges at infinity (Created page with "==Theorem== If $\mathbb{T}$ is a time scale and $s \in \mathbb{T}^+$, then $$\displaystyle\lim_{x \rightarrow \infty} \Gamma_{\mathbb{T}}(x;s) = \infty.$$ ==Proof== ==R...")
- 17:55, 15 January 2023 (diff | hist) . . (-244) . . Gamma function
- 17:54, 15 January 2023 (diff | hist) . . (+286) . . N Gamma function diverges at zero (Created page with "==Theorem== If $\mathbb{T}$ is a time scale and $s \in \mathbb{T}^+$, then $$\displaystyle\lim_{x \rightarrow 0^+} \Gamma_{\mathbb{T}}(x;s) = \infty,$$ where $\Gamma_{\mat...") (current)
- 17:54, 15 January 2023 (diff | hist) . . (-239) . . Gamma function (→Properties of gamma functions)
- 17:53, 15 January 2023 (diff | hist) . . (+19) . . Gamma function
- 17:53, 15 January 2023 (diff | hist) . . (0) . . m Convergence of gamma function at positive values (Tom moved page Convergence of gamma function to Convergence of gamma function at positive values) (current)
- 17:53, 15 January 2023 (diff | hist) . . (+62) . . N Convergence of gamma function (Tom moved page Convergence of gamma function to Convergence of gamma function at positive values) (current)
- 17:52, 15 January 2023 (diff | hist) . . (+97) . . Convergence of gamma function at positive values
- 17:52, 15 January 2023 (diff | hist) . . (+179) . . N Convergence of gamma function at positive values (Created page with "==Theorem== If $s \in \mathbb{T}^+$, then $\Gamma_{\mathbb{T}}(x;s)$ converges for any $x \in \mathbb{R}^+$. ==Proof== ==References== Category:Theorem Category:Unprov...")
- 17:51, 15 January 2023 (diff | hist) . . (-242) . . Gamma function
- 17:49, 15 January 2023 (diff | hist) . . (+62) . . Gamma function
- 17:49, 15 January 2023 (diff | hist) . . (-244) . . Gamma function
- 17:48, 15 January 2023 (diff | hist) . . (+133) . . Unilateral Laplace transform
- 17:47, 15 January 2023 (diff | hist) . . (+45) . . Paper:Martin Bohner/The gamma function on time scales (current)
- 17:47, 15 January 2023 (diff | hist) . . (+124) . . Paper:Martin Bohner/The gamma function on time scales
- 17:45, 15 January 2023 (diff | hist) . . (+1) . . Paper:Martin Bohner/The gamma function on time scales
- 17:45, 15 January 2023 (diff | hist) . . (+20) . . Paper:Martin Bohner/The gamma function on time scales
- 17:44, 15 January 2023 (diff | hist) . . (+287) . . N Paper:Martin Bohner/The gamma function on time scales (Created page with "{{Book|The gamma function on time scales|2013|Dynamics of Continuous, Discrete, and Impulsive Systems Series A: Mathematical Analysis||Martin Bohner|}} ===Online copies=== [h...")
- 17:42, 15 January 2023 (diff | hist) . . (+1) . . Forward box minus
- 17:42, 15 January 2023 (diff | hist) . . (+1) . . Gamma function
- 17:42, 15 January 2023 (diff | hist) . . (+1) . . Forward box minus
- 17:42, 15 January 2023 (diff | hist) . . (+2) . . Forward box plus
- 17:42, 15 January 2023 (diff | hist) . . (0) . . m Forward box plus (Tom moved page Forward boxplus to Forward box plus)
- 17:42, 15 January 2023 (diff | hist) . . (+30) . . N Forward boxplus (Tom moved page Forward boxplus to Forward box plus) (current)
- 17:41, 15 January 2023 (diff | hist) . . (+1) . . Forward box minus
- 17:41, 15 January 2023 (diff | hist) . . (0) . . m Forward box minus (Tom moved page Forward boxminus to Forward box minus)
- 17:41, 15 January 2023 (diff | hist) . . (+31) . . N Forward boxminus (Tom moved page Forward boxminus to Forward box minus) (current)
- 17:41, 15 January 2023 (diff | hist) . . (+44) . . Gamma function
- 17:40, 15 January 2023 (diff | hist) . . (+103) . . Gamma function
- 17:40, 15 January 2023 (diff | hist) . . (-3) . . Gamma function
- 17:40, 15 January 2023 (diff | hist) . . (+6) . . Gamma function
- 17:39, 15 January 2023 (diff | hist) . . (-156) . . Gamma function
- 17:38, 15 January 2023 (diff | hist) . . (+4) . . Forward box minus
- 17:38, 15 January 2023 (diff | hist) . . (+304) . . N Forward box minus (Created page with "Let $\mathbb{T}$ be a time scale. We define the (forward) boxminus operation $\boxminus_{\mu}$ by $$\left( p \boxplus_{\mu} q \right)(t) := \dfrac{t\Big(p(t)-q(t)\Big)}{t...")
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