User contributions
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- 19:51, 29 December 2015 (diff | hist) . . (+297) . . Hilger real part
- 19:49, 29 December 2015 (diff | hist) . . (+322) . . Hilger pure imaginary
- 19:46, 29 December 2015 (diff | hist) . . (+154) . . N Hilger real part (Created page with "Let $h>0$ and let $z \in \mathbb{C}_h$, the Hilger complex plane. The Hilger real part of $z$ is defined by $$\mathrm{Re}_h(z)=\dfrac{|zh+1|-1}{h}.$$")
- 19:45, 29 December 2015 (diff | hist) . . (+269) . . N Hilger imaginary part (Created page with "Let $h>0$ and let $z \in \mathbb{C}_h$, the Hilger complex plane. The Hilger imaginary part of $z$ is defined by $$\mathrm{Im}_h(z)=\dfrac{\mathrm{Arg}(zh+1)}{h},$$ where ...")
- 19:44, 29 December 2015 (diff | hist) . . (+49) . . Main Page (→Calculus on time scales)
- 19:43, 29 December 2015 (diff | hist) . . (+221) . . N Hilger circle (Created page with "Let $h>0$. The Hilger imaginary circle is defined by $$\mathbb{I}_h = \left\{ z \in \mathbb{C}_h \colon \left| z + \dfrac{1}{h} \right| = \dfrac{1}{h} \right\},$$ where $\math...")
- 19:41, 29 December 2015 (diff | hist) . . (+5) . . Hilger alternating axis
- 19:41, 29 December 2015 (diff | hist) . . (+188) . . N Hilger alternating axis (Created page with "The Hilger alternating axis is defined by $$\mathbb{A}_h = \{z \in \mathbb{C}_h \colon z \in \mathbb{R}, z < -\dfrac{1}{h} \right\},$$ where $\mathbb{C}_h$ is the Hilger com...")
- 19:41, 29 December 2015 (diff | hist) . . (+197) . . N Hilger real axis (Created page with "Let $h>0$. We define the Hilger real axis by $$\mathbb{R}_h = \left\{ z \in \mathbb{C}_h \colon z \in \mathbb{R}, z > -\dfrac{1}{h} \right\},$$ where $\mathbb{C}_h$ is the H...")
- 19:40, 29 December 2015 (diff | hist) . . (+141) . . N Hilger complex plane (Created page with "Let $h>0$ be fixed. We define the Hilger complex plane to be $$\mathbb{C}_h = \left\{ z \in \mathbb{C} \colon z \neq \dfrac{1}{h} \right\}.$$")
- 19:39, 29 December 2015 (diff | hist) . . (+96) . . Main Page (→Calculus on time scales)
- 19:38, 29 December 2015 (diff | hist) . . (+24) . . Main Page (→Calculus on time scales)
- 19:38, 29 December 2015 (diff | hist) . . (+371) . . Hilger pure imaginary
- 19:36, 29 December 2015 (diff | hist) . . (+243) . . N Hilger pure imaginary (Created page with "Let $h>0$ be fixed. The Hilger pure imaginary numbers, $\mathring{\iota} \omega$, where $-\dfrac{\pi}{h} < \omega \leq \dfrac{\pi}{h}$ is defined by the formula $$\mathring{\i...")
- 19:17, 29 December 2015 (diff | hist) . . (+27) . . Main Page (→Calculus on time scales)
- 19:17, 29 December 2015 (diff | hist) . . (+81) . . N Marks-Gravagne-Davis Fourier transform (Created page with " =References= [http://web.ecs.baylor.edu/faculty/gravagnei/archived/Fourier.pdf]")
- 19:15, 29 December 2015 (diff | hist) . . (+146) . . Dilation of time scales
- 19:14, 29 December 2015 (diff | hist) . . (+329) . . N Dilation of time scales (Created page with "Let $\mathbb{T}_1$ and $\mathbb{T}_2$ be time scales. Their dilation, $\mathbb{T}_1 \oplus \mathbb{T}_2$, is a time scale defined by $$\mathbb{T}_1 \oplus \mat...")
- 19:12, 29 December 2015 (diff | hist) . . (+29) . . Main Page (→Calculus on time scales)
- 21:16, 30 November 2015 (diff | hist) . . (-1) . . Delta sinh
- 04:19, 30 September 2015 (diff | hist) . . (+18) . . Delta sine
- 04:19, 30 September 2015 (diff | hist) . . (-2) . . Delta sine
- 04:19, 30 September 2015 (diff | hist) . . (-2) . . Delta sine
- 04:18, 30 September 2015 (diff | hist) . . (-6) . . Delta sine
- 02:12, 9 September 2015 (diff | hist) . . (+65) . . Integers
- 00:49, 9 September 2015 (diff | hist) . . (0) . . Unilateral Laplace transform (→Table of Laplace transforms)
- 00:45, 9 September 2015 (diff | hist) . . (+2) . . Quantum q less than 1 (current)
- 00:45, 9 September 2015 (diff | hist) . . (+2) . . Gaussian bell
- 00:45, 9 September 2015 (diff | hist) . . (-10) . . Gaussian bell
- 00:45, 9 September 2015 (diff | hist) . . (+713) . . Gaussian bell
- 00:43, 9 September 2015 (diff | hist) . . (+21) . . Integers
- 00:38, 9 September 2015 (diff | hist) . . (+98) . . Harmonic numbers (current)
- 00:36, 9 September 2015 (diff | hist) . . (+12) . . Quantum q less than 1
- 00:35, 9 September 2015 (diff | hist) . . (+81) . . Quantum q less than 1
- 00:34, 9 September 2015 (diff | hist) . . (+2) . . Quantum q less than 1
- 00:33, 9 September 2015 (diff | hist) . . (+53) . . Multiples of integers
- 00:30, 9 September 2015 (diff | hist) . . (+127) . . Real numbers
- 00:27, 9 September 2015 (diff | hist) . . (+39) . . Real numbers
- 03:05, 8 September 2015 (diff | hist) . . (-1) . . Closure of unit fractions
- 02:55, 8 September 2015 (diff | hist) . . (-3) . . Forward jump
- 02:55, 8 September 2015 (diff | hist) . . (+23) . . Forward graininess
- 02:50, 8 September 2015 (diff | hist) . . (+164) . . N Backward graininess (Created page with "Let $\mathbb{T}$ be a time scale. The backward graininess function $\nu \colon \mathbb{T}^{\kappa} \rightarrow \mathbb{T}$ is defined by $$\nu(t) = t-\rho(t).$$")
- 02:49, 8 September 2015 (diff | hist) . . (+212) . . N Backward jump (Created page with "Let $\mathbb{T}$ be a time scale. The backward jump operator $\rho \colon \mathbb{T}^{\kappa} \rightarrow \mathbb{T}$ is defined by the formula $$\rho(t) = \sup \left\{s \...")
- 21:28, 16 August 2015 (diff | hist) . . (-3) . . Closure of unit fractions
- 21:27, 16 August 2015 (diff | hist) . . (+3,744) . . Closure of unit fractions
- 21:26, 16 August 2015 (diff | hist) . . (+3,079) . . Quantum q less than 1
- 03:37, 10 August 2015 (diff | hist) . . (-1,274) . . Quantum q greater than 1
- 03:37, 10 August 2015 (diff | hist) . . (+4,711) . . Quantum q greater than 1
- 22:30, 31 July 2015 (diff | hist) . . (+196) . . N Forward graininess (Created page with "Let $\mathbb{T}$ be a time scale. The forward graininess function $\mu \colon \mathbb{T}^{\kappa}$ is defined by $$\mu(t) = \sigma(t)-t,$$ where $\sigma$ denotes the for...")
- 22:29, 31 July 2015 (diff | hist) . . (+9) . . Forward jump
- 04:47, 27 July 2015 (diff | hist) . . (0) . . Multiples of integers
- 04:47, 27 July 2015 (diff | hist) . . (+2) . . Derivation of nabla exponential T=hZ (current)
- 04:38, 27 July 2015 (diff | hist) . . (+5) . . Derivation of delta exponential T=hZ (current)
- 04:32, 27 July 2015 (diff | hist) . . (+94) . . Derivation of delta exponential T=hZ
- 04:31, 27 July 2015 (diff | hist) . . (+45) . . Derivation of nabla exponential T=hZ
- 04:27, 27 July 2015 (diff | hist) . . (+49) . . Derivation of nabla exponential T=hZ
- 03:35, 27 July 2015 (diff | hist) . . (0) . . Multiples of integers
- 03:35, 27 July 2015 (diff | hist) . . (+1,332) . . N Derivation of nabla exponential T=hZ (Created page with "Rearrange the equation $y^{\nabla}(t)=p(t)y(t);y(s)=1$ to get the equation $y(t-h)=(1-hp(t))y(t)$. From this it is clear that $$y(s+h)=\dfrac{y(s)}{1-hp(s+h)}=\displaystyle\pr...")
- 03:18, 27 July 2015 (diff | hist) . . (+1) . . Multiples of integers
- 03:17, 27 July 2015 (diff | hist) . . (0) . . Multiples of integers
- 02:27, 27 July 2015 (diff | hist) . . (+1,312) . . N Derivation of delta exponential T=hZ (Created page with "Rearrange the equation $y^{\Delta}(t)=p(t)y(t);y(s)=1$ to get the equation $y(\sigma(t))=(1+hp(t))y(t)$. From this it is clear that $$y(s+h)=(1+hp(s))y(s)=(1+hp(s))=\displayst...")
- 02:06, 27 July 2015 (diff | hist) . . (+208) . . Multiples of integers
- 14:09, 24 July 2015 (diff | hist) . . (+210) . . N Forward jump (Created page with "Let $\mathbb{T}$ be a time scale. The forward jump operator $\sigma \colon \mathbb{T} \rightarrow \mathbb{T}$ is defined by the formula $$\sigma(t) := \inf \left\{ x \in ...")
- 03:05, 16 July 2015 (diff | hist) . . (+76) . . Real numbers
- 18:52, 28 June 2015 (diff | hist) . . (+39) . . N User:Tom (Created page with "Non-robot users: Tom, ProfInsall, Pedro")
- 22:45, 27 June 2015 (diff | hist) . . (+233) . . Riccati equation
- 22:42, 27 June 2015 (diff | hist) . . (+292) . . Riccati equation
- 22:39, 27 June 2015 (diff | hist) . . (+282) . . N Disconjugate (Created page with "Let $\mathbb{T}$ be a time scale. We say that a self-adjoint equation $(py^{\Delta})^{\Delta}+qy^{\sigma}=0$ is disconjugate on an interval $[a,b] \cap \mathbb{T}$ if ...")
- 22:38, 27 June 2015 (diff | hist) . . (+18) . . Main Page (→Calculus on time scales)
- 22:38, 27 June 2015 (diff | hist) . . (+301) . . N Generalized zero (Created page with "Let $\mathbb{T}$ be a time scale. Let $(py^{\Delta})^{\Delta}+qy^{\sigma}=0$ be a self-adjoint equation. We say that a solution $y$ of the self-adjoint equation has a ...")
- 22:17, 27 June 2015 (diff | hist) . . (+3) . . Cauchy function (current)
- 21:01, 27 June 2015 (diff | hist) . . (+1) . . Cauchy function
- 06:39, 17 June 2015 (diff | hist) . . (+82) . . Time scale (→Applications of time scales)
- 11:55, 16 June 2015 (diff | hist) . . (+13) . . Multiples of integers
- 06:33, 16 June 2015 (diff | hist) . . (+75) . . Harmonic numbers
- 06:32, 16 June 2015 (diff | hist) . . (+154) . . N Derivation of forward graininess for T=Harmonic numbers (Created page with "$\begin{array}{ll} \mu(t) &= \mu \left( \displaystyle\sum_{k=1}^{n} \dfrac{1}{k} \right) \\ &= t + \dfrac{1}{n+1} - t \\ &= \dfrac{1}{n+1} \\ \end{array}$") (current)
- 06:31, 16 June 2015 (diff | hist) . . (+206) . . Harmonic numbers
- 06:28, 16 June 2015 (diff | hist) . . (+184) . . N Derivation of forward jump for T=Harmonic numbers (Created page with "$\begin{array}{ll} \sigma(t) &= \sigma \left( \displaystyle\sum_{k=1}^{n} \dfrac{1}{k} \right) \\ &= \displaystyle\sum_{k=1}^{n+1} \dfrac{1}{k} \\ &= t + \dfrac{1}{n+1} \\ \en...") (current)
- 06:25, 16 June 2015 (diff | hist) . . (+1,950) . . Harmonic numbers
- 08:11, 10 June 2015 (diff | hist) . . (+7) . . Dynamic equation
- 08:04, 10 June 2015 (diff | hist) . . (-20) . . Dynamic equation
- 08:03, 10 June 2015 (diff | hist) . . (+38) . . Dynamic equation
- 08:03, 10 June 2015 (diff | hist) . . (+40) . . Dynamic equation
- 08:02, 10 June 2015 (diff | hist) . . (-21) . . Main Page (→Calculus on time scales)
- 23:40, 9 June 2015 (diff | hist) . . (-238) . . Nabla exponential (→Examples)
- 23:40, 9 June 2015 (diff | hist) . . (-394) . . Nabla exponential (→Examples)
- 23:39, 9 June 2015 (diff | hist) . . (0) . . Derivation of nabla exponential T=isolated points (current)
- 23:36, 9 June 2015 (diff | hist) . . (+440) . . N Derivation of nabla exponential T=isolated points (Created page with "Let $\mathbb{T}$ be a time scale of isolated points. For $t>s$, find $\hat{e}_p$ by computing $$\begin{array}{ll} \hat{e}_p(t,s) &= \exp \left(-\...")
- 23:35, 9 June 2015 (diff | hist) . . (+1) . . Derivation of delta exponential T=isolated points (current)
- 23:27, 9 June 2015 (diff | hist) . . (+4) . . Derivation of delta exponential T=isolated points
- 23:27, 9 June 2015 (diff | hist) . . (+57) . . Derivation of delta exponential T=isolated points
- 23:27, 9 June 2015 (diff | hist) . . (0) . . Derivation of delta exponential T=isolated points
- 23:27, 9 June 2015 (diff | hist) . . (+355) . . N Derivation of delta exponential T=isolated points (Created page with "For $t>s$, find $e_p$ by computing $$\begin{array}{ll} e_p(t,s) &= \exp \left( \displaystyle\int_s^t \dfrac{1}{\mu(\tau)} \log(1+\mu(\tau)p(\tau)) \Delta...")
- 23:20, 9 June 2015 (diff | hist) . . (-4) . . Isolated points (current)
- 23:19, 9 June 2015 (diff | hist) . . (0) . . Isolated points
- 23:18, 9 June 2015 (diff | hist) . . (+266) . . Isolated points
- 23:11, 9 June 2015 (diff | hist) . . (+4) . . Isolated points
- 23:11, 9 June 2015 (diff | hist) . . (-1,044) . . Isolated points
- 23:01, 9 June 2015 (diff | hist) . . (+4,356) . . Isolated points
- 21:49, 9 June 2015 (diff | hist) . . (+10) . . Riccati equation
- 21:48, 9 June 2015 (diff | hist) . . (+222) . . N Riccati equation (Created page with "Let $\mathbb{T}$ be a time scale. The Riccati equation is the dynamic equation defined by $$z^{\Delta}(t) + q(t) + \dfrac{z^2(t)}{p(t)+\mu(t)z(t)}=0,$$ where $p(t)+\mu...")
- 21:47, 9 June 2015 (diff | hist) . . (+22) . . Main Page (→Calculus on time scales)
- 21:45, 9 June 2015 (diff | hist) . . (+22) . . Main Page (→Calculus on time scales)
- 21:39, 9 June 2015 (diff | hist) . . (+494) . . N Cauchy function (Created page with "Let $\mathbb{T}$ be a time scale. Consider the self-adjoint equation $(py^{\Delta})^{\Delta}+qy^{\sigma}=0$. We say that a function $\hat{y} \colon \mathbb{T} \times \...")
- 21:37, 9 June 2015 (diff | hist) . . (+21) . . Main Page (→Calculus on time scales)
- 21:29, 9 June 2015 (diff | hist) . . (+18) . . Main Page (→Calculus on time scales)
- 21:46, 22 May 2015 (diff | hist) . . (-1,059) . . Format notes (→BiBTeX)
- 01:41, 22 May 2015 (diff | hist) . . (+108) . . Bilateral Laplace transform
- 01:40, 22 May 2015 (diff | hist) . . (+308) . . N Bilateral Laplace transform (Created page with "Let $\mathbb{T}$ be a time scale. The Bilateral Laplace transform of a function $f \colon \mathbb{T} \rightarrow \mathbb{T}$ centered at $s$ is given by $$F(z,s)=\displays...")
- 01:39, 22 May 2015 (diff | hist) . . (+33) . . Main Page (→Calculus on time scales)
- 01:29, 22 May 2015 (diff | hist) . . (0) . . File:Hilgercircle,T=Z.png (Tom uploaded a new version of "File:Hilgercircle,T=Z.png") (current)
- 01:27, 22 May 2015 (diff | hist) . . (+2,729) . . Square integers (current)
- 01:24, 22 May 2015 (diff | hist) . . (+12) . . Time scales footer
- 01:24, 22 May 2015 (diff | hist) . . (+4) . . Main Page (→Calculus on time scales)
- 01:23, 22 May 2015 (diff | hist) . . (+42) . . Closure of unit fractions
- 01:23, 22 May 2015 (diff | hist) . . (+42) . . Quantum q less than 1
- 01:23, 22 May 2015 (diff | hist) . . (+42) . . Quantum q greater than 1
- 01:22, 22 May 2015 (diff | hist) . . (+42) . . Isolated points
- 01:22, 22 May 2015 (diff | hist) . . (+42) . . Harmonic numbers
- 01:22, 22 May 2015 (diff | hist) . . (+42) . . Square integers
- 01:22, 22 May 2015 (diff | hist) . . (+42) . . Multiples of integers
- 01:22, 22 May 2015 (diff | hist) . . (+42) . . Integers
- 01:21, 22 May 2015 (diff | hist) . . (+17) . . Real numbers
- 01:21, 22 May 2015 (diff | hist) . . (+1,101) . . N Time scales footer (Created page with "<table> <tr> <td colspan=9><center><h2>Time scales</h2></center></td> </tr><tr> <td><center>$\Huge\mathbb{R}$<br /> Real numbers</c...")
- 01:21, 22 May 2015 (diff | hist) . . (+25) . . Real numbers
- 01:07, 22 May 2015 (diff | hist) . . (+2,487) . . Multiples of integers
- 01:00, 22 May 2015 (diff | hist) . . (+2,205) . . Integers
- 00:46, 22 May 2015 (diff | hist) . . (0) . . m Derivation of delta sin sub p for T=Z (Tom moved page Derivation of delta sin sub p on T=Z to Derivation of delta sin sub p for T=Z) (current)
- 00:46, 22 May 2015 (diff | hist) . . (+51) . . N Derivation of delta sin sub p on T=Z (Tom moved page Derivation of delta sin sub p on T=Z to Derivation of delta sin sub p for T=Z) (current)
- 00:46, 22 May 2015 (diff | hist) . . (0) . . m Derivation of delta sin sub p for T=Z (Tom moved page Derivation of sin sub p on T=Z to Derivation of delta sin sub p on T=Z)
- 00:46, 22 May 2015 (diff | hist) . . (+50) . . N Derivation of sin sub p on T=Z (Tom moved page Derivation of sin sub p on T=Z to Derivation of delta sin sub p on T=Z) (current)
- 00:42, 22 May 2015 (diff | hist) . . (-3) . . Format notes (→General format for time scale pages)
- 00:42, 22 May 2015 (diff | hist) . . (+44) . . Format notes (→General format for time scale pages)
- 00:33, 22 May 2015 (diff | hist) . . (-4) . . Format notes (→General format for time scale pages)
- 00:32, 22 May 2015 (diff | hist) . . (+2) . . Format notes (→General format for time scale pages)
- 00:25, 22 May 2015 (diff | hist) . . (-29) . . Main Page (→Special functions on time scales)
- 00:25, 22 May 2015 (diff | hist) . . (-4) . . Main Page (→Special functions on time scales)
- 00:24, 22 May 2015 (diff | hist) . . (-22) . . Main Page
- 00:23, 22 May 2015 (diff | hist) . . (-1) . . Mozyrska-Torres logarithm (→References)
- 00:23, 22 May 2015 (diff | hist) . . (+167) . . Mozyrska-Torres logarithm
- 00:23, 22 May 2015 (diff | hist) . . (-1) . . Jackson logarithm (→References)
- 00:22, 22 May 2015 (diff | hist) . . (+172) . . Jackson logarithm
- 00:22, 22 May 2015 (diff | hist) . . (+162) . . Euler-Cauchy logarithm
- 00:22, 22 May 2015 (diff | hist) . . (+162) . . Bohner logarithm
- 00:21, 22 May 2015 (diff | hist) . . (+450) . . N Mozyrska-Torres logarithm (Created page with "Let $\mathbb{T}$ be a time scale. For $t \in \mathbb{T} \cap (0,\infty)$, define $$L_{\mathbb{T}}(t) = \displaystyle\int_1^t \dfrac{1}{\tau} \Delta \tau.$$ =Properties= *$L^{...")
- 00:20, 22 May 2015 (diff | hist) . . (+499) . . Jackson logarithm
- 00:20, 22 May 2015 (diff | hist) . . (+541) . . N Jackson logarithm (Created page with "This definition attempts to define the logarithm as the inverse of an exponential function. Let $\mathbb{T}$ be a time scale. Let $p \in \mathcal{R...")
- 00:20, 22 May 2015 (diff | hist) . . (+580) . . N Bohner logarithm (Created page with "Define the logarithm to be $$L_p(t,t_0) = \displaystyle\int_{t_0}^t \dfrac{p^{\Delta}(\tau)}{p(\tau)} \Delta \tau$$ Note while $$\dfrac{(pq)^{\Delta}}{pq} = \dfrac{p^{\Delta}...")
- 00:18, 22 May 2015 (diff | hist) . . (+31) . . Format notes
- 00:17, 22 May 2015 (diff | hist) . . (+65) . . Real numbers
- 00:15, 22 May 2015 (diff | hist) . . (+557) . . N Euler-Cauchy logarithm (Created page with "Let $\mathbb{T}$ be a time scale. Define the Euler-Cauchy logarithm to be part of a solution of the Cauchy-Euler equation $$t\sigma(t)y^{\Delta \Delta}(t) - 3ty^{\Del...")
- 00:12, 22 May 2015 (diff | hist) . . (+273) . . Real numbers
- 00:09, 22 May 2015 (diff | hist) . . (+2,427) . . Format notes (→General format for time scale pages)
- 23:55, 21 May 2015 (diff | hist) . . (+1) . . Real numbers
- 23:54, 21 May 2015 (diff | hist) . . (+447) . . Real numbers
- 23:52, 21 May 2015 (diff | hist) . . (+108) . . Main Page (→Special functions on time scales)
- 23:46, 21 May 2015 (diff | hist) . . (+1,585) . . Real numbers
- 00:01, 18 May 2015 (diff | hist) . . (+1,428) . . Format notes
- 17:23, 16 May 2015 (diff | hist) . . (0) . . Integers
- 17:16, 16 May 2015 (diff | hist) . . (+32) . . Main Page (→Calculus on time scales)
- 17:16, 16 May 2015 (diff | hist) . . (0) . . m Delta Taylor's formula (Tom moved page Taylor's formula to Delta Taylor's formula)
- 17:16, 16 May 2015 (diff | hist) . . (+36) . . N Taylor's formula (Tom moved page Taylor's formula to Delta Taylor's formula) (current)
- 02:08, 5 May 2015 (diff | hist) . . (-266) . . Nabla integral (current)
- 22:53, 4 May 2015 (diff | hist) . . (+95) . . Quantum q greater than 1
- 22:52, 4 May 2015 (diff | hist) . . (-14) . . Table:Delta hk
- 04:16, 4 May 2015 (diff | hist) . . (+1) . . N Nabla gk (Created page with "a") (current)
- 21:13, 29 April 2015 (diff | hist) . . (+65) . . Integers
- 20:52, 29 April 2015 (diff | hist) . . (+5) . . Integers
- 20:51, 29 April 2015 (diff | hist) . . (-4) . . Integers
- 20:49, 29 April 2015 (diff | hist) . . (+187) . . Integers
- 20:44, 29 April 2015 (diff | hist) . . (+1) . . Derivation of delta sin sub p for T=Z
- 20:43, 29 April 2015 (diff | hist) . . (+284) . . Derivation of delta sin sub p for T=Z
- 20:37, 29 April 2015 (diff | hist) . . (-4) . . Derivation of delta sin sub p for T=Z
- 20:37, 29 April 2015 (diff | hist) . . (+157) . . Integers
- 20:36, 29 April 2015 (diff | hist) . . (+185) . . N Derivation of delta sin sub p for T=Z (Created page with "$$\begin{array}{ll} \sin_p(t,s) &= \dfrac{e_{ip}(t,s)-e_{-ip}(t,s)}{2i} \\ &= \dfrac{\displaystyle\prod_{k=t_0}^{t-1}1+ip(k) - \displaystyle\prod_{k=t_0}^{t-1}1-ip(k)}{2i} \en...")
- 19:38, 29 April 2015 (diff | hist) . . (-13) . . Real numbers
- 19:36, 29 April 2015 (diff | hist) . . (-9) . . Real numbers
- 19:33, 29 April 2015 (diff | hist) . . (+512) . . N Derivation of delta e sub p on T=Z (Created page with "If $t>s$, then $$\begin{array}{ll} e_p(t,s) &= \exp \left( \displaystyle\int_{s}^{t} \dfrac{1}{\mu(\tau)} \log(1 + p(\tau)) \Delta \tau \right) \\ &= \exp \left( \displaystyle...") (current)
- 19:31, 29 April 2015 (diff | hist) . . (-211) . . Integers
- 19:26, 29 April 2015 (diff | hist) . . (+430) . . Real numbers
- 19:13, 29 April 2015 (diff | hist) . . (+389) . . N Derivation of delta exponential T=R (Created page with "$\begin{array}{ll} e_p(t,s) &= \exp \left( \displaystyle\int_s^t \displaystyle\lim_{h \rightarrow 0} \dfrac{1}{h} \log(1 + hp(\tau)) d\tau \right) \\ &\hspace{-10pt} \stackrel...") (current)
- 19:13, 29 April 2015 (diff | hist) . . (-349) . . Real numbers
- 19:12, 29 April 2015 (diff | hist) . . (0) . . Real numbers
- 07:24, 29 April 2015 (diff | hist) . . (+75) . . Real numbers
- 07:22, 29 April 2015 (diff | hist) . . (+878) . . N Examples of time scales (Created page with "==Examples of time scales== # The real line: $\mathbb{R}$ # The integers: $\mathbb{Z} = \{\ldots, -1,0,1,\ldots\}$ # Multiples of integer...") (current)
- 07:22, 29 April 2015 (diff | hist) . . (-846) . . Main Page
- 05:29, 26 April 2015 (diff | hist) . . (+8) . . Expected value (→Properties)
- 05:17, 26 April 2015 (diff | hist) . . (-18) . . Expected value
- 03:18, 26 April 2015 (diff | hist) . . (-8) . . Convergence of time scales (current)
- 01:30, 17 April 2015 (diff | hist) . . (+34) . . Main Page (→Calculus on time scales)
- 22:14, 14 April 2015 (diff | hist) . . (+36) . . Variance (→Examples)
- 22:14, 14 April 2015 (diff | hist) . . (+42) . . Expected value
- 22:13, 14 April 2015 (diff | hist) . . (+331) . . N Variance of gamma distribution (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $X$ have the gamma distribution o...") (current)
- 22:13, 14 April 2015 (diff | hist) . . (+333) . . N Expected value of gamma distribution (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $X$ have the gamma distributi...") (current)
- 22:13, 14 April 2015 (diff | hist) . . (+192) . . Gamma distribution
- 22:05, 14 April 2015 (diff | hist) . . (+42) . . Variance (→Examples)
- 22:04, 14 April 2015 (diff | hist) . . (+48) . . Expected value
- 22:04, 14 April 2015 (diff | hist) . . (+343) . . N Variance of exponential distribution (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $X$ have the exponential dist...")
- 22:04, 14 April 2015 (diff | hist) . . (+345) . . N Expected value of exponential distribution (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $X$ have the exponentia...")
- 22:03, 14 April 2015 (diff | hist) . . (-513) . . Exponential distribution
- 22:02, 14 April 2015 (diff | hist) . . (+50) . . Variance
- 22:02, 14 April 2015 (diff | hist) . . (-16) . . Variance
- 22:01, 14 April 2015 (diff | hist) . . (+55) . . Expected value
- 22:00, 14 April 2015 (diff | hist) . . (0) . . Variance of uniform distribution (current)
- 22:00, 14 April 2015 (diff | hist) . . (+9) . . Expected value of uniform distribution
- 21:59, 14 April 2015 (diff | hist) . . (+18) . . Exponential distribution (→Properties)
- 21:59, 14 April 2015 (diff | hist) . . (-18) . . Exponential distribution (→Properties)
- 21:58, 14 April 2015 (diff | hist) . . (+19) . . Exponential distribution
- 21:58, 14 April 2015 (diff | hist) . . (+37) . . Exponential distribution
- 21:57, 14 April 2015 (diff | hist) . . (+602) . . Exponential distribution
- 21:53, 14 April 2015 (diff | hist) . . (0) . . Uniform distribution
- 21:53, 14 April 2015 (diff | hist) . . (+88) . . Exponential distribution
- 21:52, 14 April 2015 (diff | hist) . . (+73) . . Uniform distribution
- 21:49, 14 April 2015 (diff | hist) . . (+434) . . N Variance of uniform distribution (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Proposition:</strong> Let $X$ have the uniform distribu...")
- 21:48, 14 April 2015 (diff | hist) . . (+366) . . N Expected value of uniform distribution (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Proposition:</strong> Let $X$ have the uniform di...")
- 21:47, 14 April 2015 (diff | hist) . . (+96) . . Uniform distribution
- 21:44, 14 April 2015 (diff | hist) . . (+81) . . Probability density function (current)
- 16:40, 14 April 2015 (diff | hist) . . (+310) . . Expected value
- 07:02, 14 April 2015 (diff | hist) . . (+529) . . N Nabla hk (Created page with "Define the $\hat{h}_k$ monomials by $$\left\{ \begin{array}{ll} \hat{h}_0(t,s)=0 \\ \hat{h}_{n+1}(t,s)=\displaystyle\int_s^t \hat{h}_n(\tau,s) \nabla \tau. \end{array} \right....") (current)
- 06:23, 14 April 2015 (diff | hist) . . (+1) . . Nabla exponential
- 21:56, 13 April 2015 (diff | hist) . . (+3,217) . . N Duality of delta and nabla (Created page with "Let $\mathbb{T}$ be a time scale. Define the dual time scale $\mathbb{T}^*=\{s \in \mathbb{R} \colon -s \in \mathbb{T} \}$, which is a time scale. We label the basic time ...") (current)
- 21:38, 13 April 2015 (diff | hist) . . (+21) . . Main Page (→Calculus on time scales)
- 21:38, 13 April 2015 (diff | hist) . . (+24) . . Main Page (→Calculus on time scales)
- 09:29, 12 April 2015 (diff | hist) . . (+2) . . Relationship between delta exponential and nabla exponential
- 09:26, 12 April 2015 (diff | hist) . . (+2) . . Relationship between nabla exponential and delta exponential
- 09:25, 12 April 2015 (diff | hist) . . (+22) . . Main Page (→Calculus on time scales)
- 09:16, 12 April 2015 (diff | hist) . . (+133) . . Nabla exponential (→Properties of $\nabla$-exponential functions)
- 09:15, 12 April 2015 (diff | hist) . . (-3) . . Delta exponential (→Properties of $\Delta$-exponential Functions)
- 09:15, 12 April 2015 (diff | hist) . . (+137) . . Relationship between nabla exponential and delta exponential
- 09:15, 12 April 2015 (diff | hist) . . (+131) . . Relationship between delta exponential and nabla exponential
- 09:14, 12 April 2015 (diff | hist) . . (+388) . . N Relationship between nabla exponential and delta exponential (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> If $p$ is [...")
- 09:13, 12 April 2015 (diff | hist) . . (+98) . . Delta exponential (→Properties of $\Delta$-exponential Functions)
- 09:12, 12 April 2015 (diff | hist) . . (+420) . . N Relationship between delta exponential and nabla exponential (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $p \in ...")
- 09:12, 12 April 2015 (diff | hist) . . (+102) . . Delta exponential (→Properties of $\Delta$-exponential Functions)
- 09:06, 12 April 2015 (diff | hist) . . (+129) . . Nabla derivative (→Properties of the $\nabla$-derivative)
- 09:06, 12 April 2015 (diff | hist) . . (+606) . . N Relationship between delta derivative and nabla derivative (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{...")
- 09:05, 12 April 2015 (diff | hist) . . (+63) . . Relationship between nabla derivative and delta derivative
- 09:05, 12 April 2015 (diff | hist) . . (+515) . . N Relationship between nabla derivative and delta derivative (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarro...")
- 09:05, 12 April 2015 (diff | hist) . . (+129) . . Delta derivative (→Properties of the $\Delta$-derivativeBohner, Martin ; Peterson, Allan. Dynamic equations on time scales. An introduction with applications. Birkhäuser Boston, Inc., Boston, MA, 2001,p.8.)
- 08:32, 12 April 2015 (diff | hist) . . (+788) . . Diamond alpha derivative (current)
- 08:28, 12 April 2015 (diff | hist) . . (+473) . . Diamond alpha derivative
- 08:23, 12 April 2015 (diff | hist) . . (+61) . . Diamond alpha derivative
- 18:37, 6 April 2015 (diff | hist) . . (+1,084) . . N Chain rule (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Assume that $g \colon \mathbb{R} \rightarrow \mathbb{R}$ is continuous, $g \...") (current)
- 18:32, 6 April 2015 (diff | hist) . . (+16) . . Main Page (→Calculus on time scales)
- 06:37, 6 April 2015 (diff | hist) . . (+850) . . N Induction on time scales (Created page with "Let $\mathbb{T}$ be a time scale. <div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $t_0 \in \mathbb{T}$ and assume t...")
- 06:32, 6 April 2015 (diff | hist) . . (+30) . . Main Page (→Calculus on time scales)
- 19:33, 5 April 2015 (diff | hist) . . (-295) . . Main Page
- 19:28, 5 April 2015 (diff | hist) . . (+297) . . Abel dynamic equation (current)
- 05:57, 5 April 2015 (diff | hist) . . (+68) . . Time scale
- 05:55, 5 April 2015 (diff | hist) . . (-87) . . Time scale
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