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- 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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