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- 08:07, 1 June 2016 (diff | hist) . . (0) . . Delta exponential
- 08:02, 1 June 2016 (diff | hist) . . (+130) . . Delta sinh
- 08:01, 1 June 2016 (diff | hist) . . (+836) . . N File:Integerdeltasinh,a=0.6,s=0plot.png (Category:plot Category:deltasinh Category:timescale:integers Category:specialfunction <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] =...) (current)
- 07:57, 1 June 2016 (diff | hist) . . (+126) . . Delta cosh
- 07:55, 1 June 2016 (diff | hist) . . (+798) . . N File:Integercosh,a=0.6,s=0plot.png (Category:plot Category:deltaexponential Category:timescale:integers Category:specialfunction <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figs...) (current)
- 07:54, 1 June 2016 (diff | hist) . . (+34) . . Format notes (→Categories) (current)
- 07:54, 1 June 2016 (diff | hist) . . (-9) . . Format notes (→Categories)
- 07:48, 1 June 2016 (diff | hist) . . (+108) . . Delta special functions footer
- 07:47, 1 June 2016 (diff | hist) . . (+4) . . File:Integerdeltacosine,a=0.6,s=0glyph.png (current)
- 07:46, 1 June 2016 (diff | hist) . . (+1,158) . . N File:Integerdeltacosine,a=0.6,s=0glyph.png (Category:deltasineglyph Category:glyph Category:timescale:integers Category:deltasine <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] =...)
- 07:45, 1 June 2016 (diff | hist) . . (+116) . . Format notes (→Categories)
- 07:25, 1 June 2016 (diff | hist) . . (+5) . . File:Integerdeltacosine,a=0.6,s=0plot.png (current)
- 07:25, 1 June 2016 (diff | hist) . . (0) . . m File:Integerdeltacosine,a=0.6,s=0plot.png (Tom moved page File:Integercosine,a=0.6,s=0plot.png to File:Integerdeltacosine,a=0.6,s=0plot.png)
- 07:25, 1 June 2016 (diff | hist) . . (+55) . . N File:Integercosine,a=0.6,s=0plot.png (Tom moved page File:Integercosine,a=0.6,s=0plot.png to File:Integerdeltacosine,a=0.6,s=0plot.png) (current)
- 07:24, 1 June 2016 (diff | hist) . . (+132) . . Delta cosine
- 07:24, 1 June 2016 (diff | hist) . . (+909) . . N File:Integerdeltacosine,a=0.6,s=0plot.png (Category:plot Category:deltacosine Category:timescale:integers Category:specialfunction <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize']...)
- 07:14, 1 June 2016 (diff | hist) . . (-63) . . Delta special functions footer
- 07:14, 1 June 2016 (diff | hist) . . (+106) . . Delta special functions footer
- 07:11, 1 June 2016 (diff | hist) . . (+1,155) . . N File:Integerdeltasine,a=0.6,s=0glyph.png (Category:deltasineglyph Category:glyph Category:timescale:integers Category:deltasine <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] =...) (current)
- 07:00, 1 June 2016 (diff | hist) . . (+132) . . Delta sine
- 07:00, 1 June 2016 (diff | hist) . . (-187) . . Format notes (→Galleries)
- 06:59, 1 June 2016 (diff | hist) . . (+486) . . Format notes
- 06:59, 1 June 2016 (diff | hist) . . (+943) . . N File:Integerdeltasine,a=0.6,s=0plot.png (Category:Plot Category:TimeScaleDeltaExponential Category:TimeScale:Integers Category:SpecialFunction <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['fi...) (current)
- 06:56, 1 June 2016 (diff | hist) . . (+53) . . N File:Integersine,a=0.6,s=0plot.png (Tom moved page File:Integersine,a=0.6,s=0plot.png to File:Integerdeltasine,a=0.6,s=0plot.png) (current)
- 06:55, 1 June 2016 (diff | hist) . . (+29) . . Format notes (→Categories)
- 00:36, 1 June 2016 (diff | hist) . . (+39) . . Delta special functions footer
- 00:33, 1 June 2016 (diff | hist) . . (+1,059) . . N File:Integerdeltaexponential,a=-3,s=0glyph.png (Category:deltaexponentialglyph Category:glyph Category:timeScale:integers Category:deltaexponential <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['fig...) (current)
- 23:57, 31 May 2016 (diff | hist) . . (+95) . . Delta special functions footer
- 23:53, 31 May 2016 (diff | hist) . . (+37) . . Main Page (→$\Delta$-calculus)
- 23:52, 31 May 2016 (diff | hist) . . (+1,050) . . N File:Integerdeltaexponential,a=1,s=0glyph.png (Category:deltaexponentialglyph Category:glyph Category:timeScale:integers Category:deltaexponential <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figu...) (current)
- 23:35, 31 May 2016 (diff | hist) . . (+40) . . Forward circle minus
- 23:35, 31 May 2016 (diff | hist) . . (+425) . . Forward circle minus
- 23:28, 31 May 2016 (diff | hist) . . (0) . . Forward regressive
- 23:28, 31 May 2016 (diff | hist) . . (0) . . m Forward regressive (Tom moved page Regressive function to Forward regressive function)
- 23:28, 31 May 2016 (diff | hist) . . (+41) . . N Regressive function (Tom moved page Regressive function to Forward regressive function) (current)
- 23:28, 31 May 2016 (diff | hist) . . (+21) . . Forward circle minus
- 23:27, 31 May 2016 (diff | hist) . . (+91) . . Forward circle minus
- 23:25, 31 May 2016 (diff | hist) . . (0) . . m Forward circle minus (Tom moved page Circle minus to Forward circle minus)
- 23:25, 31 May 2016 (diff | hist) . . (+34) . . N Circle minus (Tom moved page Circle minus to Forward circle minus) (current)
- 23:24, 31 May 2016 (diff | hist) . . (+40) . . Delta exponential
- 23:20, 31 May 2016 (diff | hist) . . (+33) . . Quotient of delta exponentials with fixed t and s
- 23:20, 31 May 2016 (diff | hist) . . (+33) . . Product of delta exponentials with fixed t and s
- 23:19, 31 May 2016 (diff | hist) . . (+22) . . Reciprocal of delta exponential
- 23:14, 31 May 2016 (diff | hist) . . (+4) . . Semigroup property of delta exponential
- 23:13, 31 May 2016 (diff | hist) . . (+4) . . Delta exponential with p=0
- 23:13, 31 May 2016 (diff | hist) . . (+4) . . Delta exponential with t=s
- 23:13, 31 May 2016 (diff | hist) . . (+4) . . Delta simple useful formula
- 23:13, 31 May 2016 (diff | hist) . . (-357) . . Delta exponential
- 23:12, 31 May 2016 (diff | hist) . . (+517) . . N Quotient of delta exponentials with fixed t and s (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a ...")
- 23:11, 31 May 2016 (diff | hist) . . (-266) . . Delta exponential
- 23:09, 31 May 2016 (diff | hist) . . (-2) . . Reciprocal of delta exponential
- 23:09, 31 May 2016 (diff | hist) . . (-4) . . Reciprocal of delta exponential
- 23:09, 31 May 2016 (diff | hist) . . (-4) . . Product of delta exponentials with fixed t and s
- 23:09, 31 May 2016 (diff | hist) . . (+564) . . N Product of delta exponentials with fixed t and s (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a [...")
- 23:07, 31 May 2016 (diff | hist) . . (-256) . . Delta exponential
- 23:06, 31 May 2016 (diff | hist) . . (+525) . . N Reciprocal of delta exponential (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a time scale, le...")
- 23:04, 31 May 2016 (diff | hist) . . (-272) . . Delta exponential
- 23:03, 31 May 2016 (diff | hist) . . (0) . . m Delta simple useful formula (Tom moved page Simple useful formula to Delta simple useful formula)
- 23:03, 31 May 2016 (diff | hist) . . (+41) . . N Simple useful formula (Tom moved page Simple useful formula to Delta simple useful formula) (current)
- 23:03, 31 May 2016 (diff | hist) . . (+6) . . Delta exponential
- 23:02, 31 May 2016 (diff | hist) . . (+584) . . N Delta simple useful formula (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a time scale, $t,s \in \ma...")
- 23:00, 31 May 2016 (diff | hist) . . (-342) . . Delta exponential
- 22:58, 31 May 2016 (diff | hist) . . (-76) . . Delta exponential
- 22:56, 31 May 2016 (diff | hist) . . (+447) . . N Delta exponential with t=s (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a time scale, $t \in ...")
- 22:55, 31 May 2016 (diff | hist) . . (+381) . . N Delta exponential with p=0 (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a time scale and $t,s...")
- 22:52, 31 May 2016 (diff | hist) . . (-235) . . Delta exponential
- 22:51, 31 May 2016 (diff | hist) . . (+6) . . Delta exponential
- 22:51, 31 May 2016 (diff | hist) . . (+11) . . Delta exponential
- 22:51, 31 May 2016 (diff | hist) . . (+103) . . Delta exponential
- 22:49, 31 May 2016 (diff | hist) . . (+11) . . Semigroup property of delta exponential
- 22:48, 31 May 2016 (diff | hist) . . (+2) . . Semigroup property of delta exponential
- 22:48, 31 May 2016 (diff | hist) . . (0) . . Semigroup property of delta exponential
- 22:48, 31 May 2016 (diff | hist) . . (+504) . . N Semigroup property of delta exponential (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a time sca...")
- 22:46, 31 May 2016 (diff | hist) . . (-269) . . Delta exponential
- 22:45, 31 May 2016 (diff | hist) . . (+9) . . Delta exponential
- 22:45, 31 May 2016 (diff | hist) . . (+72) . . Delta exponential
- 22:44, 31 May 2016 (diff | hist) . . (+1,027) . . N File:Integerexponential,a=2,s=1plot.png (Category:Plot Category:TimeScaleDeltaExponential Category:TimeScale:Integers <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] = 10, 10 x=n...) (current)
- 22:37, 31 May 2016 (diff | hist) . . (+1,025) . . N File:Integerexponential,a=2,s=0plot.png (Category:Plot Category:TimeScaleDeltaExponential Category:TimeScale:Integers <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] = 10, 10 x=n...) (current)
- 22:32, 31 May 2016 (diff | hist) . . (+72) . . Delta exponential
- 22:29, 31 May 2016 (diff | hist) . . (-1) . . Delta exponential
- 22:29, 31 May 2016 (diff | hist) . . (+124) . . Delta exponential
- 22:24, 31 May 2016 (diff | hist) . . (+116) . . Format notes
- 22:24, 31 May 2016 (diff | hist) . . (+5) . . File:Integerexponential,a=2,s=-1plot.png (current)
- 22:23, 31 May 2016 (diff | hist) . . (+32) . . File:Integerexponential,a=2,s=-1plot.png
- 22:23, 31 May 2016 (diff | hist) . . (+962) . . N File:Integerexponential,a=2,s=-1plot.png (Category:Plot Category:TimeScaleExponential <pre>#!/usr/bin/python import numpy as np import matplotlib.pyplot as plt from mpmath import * from pylab import rcParams rcParams['figure.figsize'] = 10, 10 x=np.arange(-3,4,1); x2=np.arange(-20,20,...)
- 22:02, 31 May 2016 (diff | hist) . . (-8) . . Time scale
- 22:00, 31 May 2016 (diff | hist) . . (-105) . . Delta exponential
- 21:59, 31 May 2016 (diff | hist) . . (+10) . . Delta exponential
- 01:12, 5 April 2016 (diff | hist) . . (+5) . . Main Page (→$\nabla$-calculus)
- 01:10, 5 April 2016 (diff | hist) . . (-14) . . Main Page (→$\nabla$-calculus)
- 01:05, 5 April 2016 (diff | hist) . . (-7) . . Main Page (→$\Delta$-calculus)
- 01:04, 5 April 2016 (diff | hist) . . (-14) . . Main Page (→$\Delta$-calculus)
- 05:30, 16 March 2016 (diff | hist) . . (+131) . . Main Page
- 05:53, 27 February 2016 (diff | hist) . . (-456) . . Delta derivative
- 05:06, 26 February 2016 (diff | hist) . . (-46) . . Main Page (→Special functions on time scales)
- 22:47, 23 February 2016 (diff | hist) . . (-754) . . Time scale
- 22:41, 23 February 2016 (diff | hist) . . (+42) . . Nth root of nonnegative integers
- 22:39, 23 February 2016 (diff | hist) . . (+32) . . Right dense point
- 22:38, 23 February 2016 (diff | hist) . . (+191) . . N Right scattered point (Created page with "Let $\mathbb{T}$ be a time scale. We say that $t \in \mathbb{T}$ is a right scattered point if $\sigma(t)>t$. We say that $t$ is left scattered if $\rho(t)<t$. =See Also=...")
- 22:37, 23 February 2016 (diff | hist) . . (+21) . . Main Page (→Calculus on time scales)
- 22:32, 23 February 2016 (diff | hist) . . (+119) . . Closure of unit fractions (current)
- 22:29, 23 February 2016 (diff | hist) . . (+84) . . N Cantor set (Created page with "The [http://hyperspacewiki.org/index.php/Cantor_set Cantor set] is a time scale.") (current)
- 22:29, 23 February 2016 (diff | hist) . . (+16) . . Time scales footer (current)
- 22:27, 23 February 2016 (diff | hist) . . (+76) . . Nth root of nonnegative integers
- 22:22, 23 February 2016 (diff | hist) . . (+97) . . Nth root of nonnegative integers
- 22:18, 23 February 2016 (diff | hist) . . (+17) . . Nth root of nonnegative integers
- 22:18, 23 February 2016 (diff | hist) . . (+75) . . Nth root of nonnegative integers
- 22:16, 23 February 2016 (diff | hist) . . (+4,645) . . N Nth root of nonnegative integers (Created page with "The set $\sqrt[n]{\mathbb{N}_0}=\{0,1,\sqrt[n]{2}, \sqrt[n]{3},\ldots\}$ is a time scale. {| class="wikitable" |+$\mathbb{T}=\sqrt[n]{\mathbb{N}}$ |- |Forward jump: |...")
- 22:13, 23 February 2016 (diff | hist) . . (-3) . . Time scales footer
- 22:00, 19 February 2016 (diff | hist) . . (+754) . . Jackson logarithm (→Properties)
- 04:14, 19 February 2016 (diff | hist) . . (+387) . . N Pre-differentiable (Created page with "Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. We say that $f$ is pre-differentiable with region of differentiation $D \subset \mat...")
- 04:00, 19 February 2016 (diff | hist) . . (+24) . . Main Page (→Calculus on time scales)
- 03:59, 19 February 2016 (diff | hist) . . (+282) . . Rd-continuous
- 03:57, 19 February 2016 (diff | hist) . . (+363) . . N Rd-continuous (Created page with "Let $\mathbb{T}$ be a time scale and $f \colon \mathbb{T} \rightarrow \mathbb{R}$ be a regulated function. We say that $f$ is rd-continuous if for any dense point|ri...")
- 03:55, 19 February 2016 (diff | hist) . . (+19) . . Main Page (→Calculus on time scales)
- 03:54, 19 February 2016 (diff | hist) . . (+17) . . Main Page (→Calculus on time scales)
- 03:53, 19 February 2016 (diff | hist) . . (+244) . . N Right dense point (Created page with "Let $\mathbb{T}$ be a time scale. We say that $t \in \mathbb{T}$ is right dense if the forward jump operator obeys the formula $\sigma(t)=t$. We say that $t$ is left d...")
- 03:52, 19 February 2016 (diff | hist) . . (+352) . . N Regulated (Created page with "Let $\mathbb{T}$ be a time scale and let $f \colon \mathbb{T} \rightarrow \mathbb{R}$. We say that $f$ is regulated if for all right dense points $t_1 \in ...")
- 03:49, 19 February 2016 (diff | hist) . . (+24) . . Main Page (→Calculus on time scales)
- 01:32, 19 February 2016 (diff | hist) . . (+185) . . Time scales footer
- 01:26, 19 February 2016 (diff | hist) . . (+78) . . Time scales footer
- 01:24, 19 February 2016 (diff | hist) . . (+81) . . Time scales footer
- 01:23, 19 February 2016 (diff | hist) . . (0) . . m Euler-Cauchy logarithm (Tom moved page Euler-Cauchy logarithm to Cauchy-Euler logarithm)
- 01:14, 19 February 2016 (diff | hist) . . (+164) . . Integers (current)
- 01:13, 19 February 2016 (diff | hist) . . (+77) . . N Derivation of delta exponential T=Z (Created page with "The proof is the same as Derivation of delta exponential T=hZ with $h=1$.") (current)
- 18:42, 8 February 2016 (diff | hist) . . (+448) . . Shifting problem
- 18:41, 8 February 2016 (diff | hist) . . (-386) . . Unilateral convolution
- 18:37, 8 February 2016 (diff | hist) . . (0) . . Unilateral convolution
- 18:36, 8 February 2016 (diff | hist) . . (+2) . . Unilateral convolution
- 18:35, 8 February 2016 (diff | hist) . . (+33) . . Unilateral convolution
- 18:35, 8 February 2016 (diff | hist) . . (+34) . . Shifting problem
- 14:35, 8 February 2016 (diff | hist) . . (+443) . . Shifting problem
- 14:33, 8 February 2016 (diff | hist) . . (+390) . . Unilateral convolution
- 14:07, 8 February 2016 (diff | hist) . . (+2,170) . . Unilateral convolution
- 06:12, 8 February 2016 (diff | hist) . . (-332) . . Unilateral convolution
- 06:12, 8 February 2016 (diff | hist) . . (+1,438) . . N Unilateral convolution (Created page with "Let $f,g \colon \mathbb{R} \rightarrow \mathbb{R}$ be Lebesgue integrable on $\mathbb{R}$. The classical (i.e. time scale $\mathbb{T}=\mathbb{R}$) convolution of $f$ a...")
- 06:06, 8 February 2016 (diff | hist) . . (+22) . . Main Page (→Calculus on time scales)
- 06:05, 8 February 2016 (diff | hist) . . (+520) . . N Shifting problem (Created page with "Let $\mathbb{T}$ be a time scale, $t_0 \in \mathbb{T}$, and $f \colon [t_0,\infty) \cap \mathbb{T} \rightarrow \mathbb{C}$. The shifting problem is the following partial dyn...")
- 05:46, 8 February 2016 (diff | hist) . . (+17) . . Main Page (→Calculus on time scales)
- 18:17, 29 January 2016 (diff | hist) . . (+34) . . Timescalewiki:About (current)
- 20:18, 29 December 2015 (diff | hist) . . (+74) . . Marks-Gravagne-Davis Fourier transform
- 20:17, 29 December 2015 (diff | hist) . . (+422) . . Marks-Gravagne-Davis Fourier transform
- 20:06, 29 December 2015 (diff | hist) . . (+40) . . Forward circle plus (→Properties)
- 20:05, 29 December 2015 (diff | hist) . . (+377) . . N Circle minus inverse of circle plus (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> The circle minus $\ominus_h$ is ...")
- 20:05, 29 December 2015 (diff | hist) . . (-297) . . Forward circle minus (→Properties)
- 20:04, 29 December 2015 (diff | hist) . . (+498) . . N Forward circle minus (Created page with "Let $h>0$ and $z_1,z_2 \in \mathbb{C}_h$, the Hilger complex plane. We define the $\ominus_h$ operation by $$\ominus_h z = \dfrac{-z}{1+zh}.$$ =Properties= <div class="to...")
- 20:02, 29 December 2015 (diff | hist) . . (+60) . . Hilger pure imaginary
- 20:02, 29 December 2015 (diff | hist) . . (+60) . . Forward circle plus (→Properties)
- 20:02, 29 December 2015 (diff | hist) . . (+59) . . Hilger imaginary part (→Properties)
- 20:01, 29 December 2015 (diff | hist) . . (+110) . . Hilger real part oplus Hilger imaginary part equals z
- 20:00, 29 December 2015 (diff | hist) . . (+409) . . N Forward circle plus (Created page with "Let $h>0$ and $z_1,z_2 \in \mathbb{C}_h$, the Hilger complex plane. Then we define the $\oplus_h$ operation by $$z_1 \oplus_h z_2 = z_1+z_2+z_1 z_2h.$$ =Properties= <div ...")
- 19:58, 29 December 2015 (diff | hist) . . (+35) . . Main Page (→Calculus on time scales)
- 19:57, 29 December 2015 (diff | hist) . . (+461) . . N Hilger real part oplus Hilger imaginary part equals z (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> The following formula holds: $$z = \mathrm{Re}_h(z) \oplus \mathring{\iota} ...")
- 19:56, 29 December 2015 (diff | hist) . . (+59) . . Hilger real part
- 19:55, 29 December 2015 (diff | hist) . . (+59) . . Hilger imaginary part (→Properties)
- 19:54, 29 December 2015 (diff | hist) . . (+128) . . Limit of Hilger real and imag parts yields classical
- 19:54, 29 December 2015 (diff | hist) . . (+411) . . N Limit of Hilger real and imag parts yields classical (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> The following formu...")
- 19:53, 29 December 2015 (diff | hist) . . (+59) . . Hilger real part
- 19:52, 29 December 2015 (diff | hist) . . (+310) . . Hilger imaginary part
- 19:51, 29 December 2015 (diff | hist) . . (+297) . . Hilger real part
- 19:49, 29 December 2015 (diff | hist) . . (+322) . . Hilger pure imaginary
- 19:46, 29 December 2015 (diff | hist) . . (+154) . . N Hilger real part (Created page with "Let $h>0$ and let $z \in \mathbb{C}_h$, the Hilger complex plane. The Hilger real part of $z$ is defined by $$\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
- 05:55, 5 April 2015 (diff | hist) . . (-158) . . Time scale
- 21:26, 29 March 2015 (diff | hist) . . (+124) . . Delta heat equation
- 21:26, 29 March 2015 (diff | hist) . . (+124) . . Delta wave equation
- 10:00, 29 March 2015 (diff | hist) . . (+27) . . Delta heat equation
- 10:00, 29 March 2015 (diff | hist) . . (+259) . . N Delta wave equation (Created page with "Let $\mathbb{T}_1$ and $\mathbb{T}_2$ be time scales and $c \in \mathbb{R}$. Define the wave equation by $$u^{\Delta_1^2}=c^2 u^{\Delta_2^2},$$ where $\Delta_1...")
- 09:59, 29 March 2015 (diff | hist) . . (+50) . . Main Page (→$\Delta$-calculus)
- 09:59, 29 March 2015 (diff | hist) . . (+25) . . Main Page (→$\Delta$-calculus)
- 09:59, 29 March 2015 (diff | hist) . . (-6) . . Main Page (→$\Delta$-calculus)
- 09:58, 29 March 2015 (diff | hist) . . (+33) . . N Heat equation (Tom moved page Heat equation to Delta heat equation) (current)
- 09:58, 29 March 2015 (diff | hist) . . (0) . . m Delta heat equation (Tom moved page Heat equation to Delta heat equation)
- 09:58, 29 March 2015 (diff | hist) . . (0) . . m Delta heat equation (Tom moved page Homogeneous heat operator to Heat equation)
- 09:58, 29 March 2015 (diff | hist) . . (+27) . . N Homogeneous heat operator (Tom moved page Homogeneous heat operator to Heat equation) (current)
- 09:58, 29 March 2015 (diff | hist) . . (+234) . . N Delta heat equation (Created page with "Let $\mathbb{T}_1$ and $\mathbb{T}_2$ be time scales. Define the heat equation by $$u^{\Delta_1}=c^2 u^{\Delta_2^2},$$ where $\Delta_1$ and $\Delta_2$ denote [...")
- 09:55, 29 March 2015 (diff | hist) . . (+31) . . Main Page (→$\Delta$-calculus)
- 09:51, 29 March 2015 (diff | hist) . . (+222) . . N Partial Delta Dynamic Equations (Created page with "=References= [http://ac.els-cdn.com/S0377042705001019/1-s2.0-S0377042705001019-main.pdf?_tid=10aec9d0-d5f9-11e4-95d2-00000aab0f01&acdnat=1427622823_40bf4701ab7ec8aa1698a42c857...") (current)
- 09:51, 29 March 2015 (diff | hist) . . (+74) . . Main Page (→$\Delta$-calculus)
- 08:42, 29 March 2015 (diff | hist) . . (+25) . . Directional Delta Derivative (current)
- 08:41, 29 March 2015 (diff | hist) . . (+79) . . Directional Delta Derivative
- 08:25, 29 March 2015 (diff | hist) . . (+224) . . Directional Delta Derivative
- 07:48, 29 March 2015 (diff | hist) . . (+37) . . Main Page (→$\Delta$-calculus)
- 07:48, 29 March 2015 (diff | hist) . . (+771) . . Partial delta derivative
- 07:41, 29 March 2015 (diff | hist) . . (+99) . . Directional Delta Derivative
- 07:40, 29 March 2015 (diff | hist) . . (+983) . . N Directional Delta Derivative (Created page with "Let $\mathbb{T}_1$ and $\mathbb{T}_2$ be time scales. Let $f \colon \mathbb{T}_1 \times \mathbb{T}_2 \rightarrow \mathbb{R}$. The directional delta derivative of $f$ at th...")
- 07:35, 29 March 2015 (diff | hist) . . (+68) . . Main Page (→$\Delta$-calculus)
- 07:29, 29 March 2015 (diff | hist) . . (+98) . . N Partial delta derivative (Created page with " =References= [http://web.mst.edu/~bohner/papers/pdots.pdf Partial differentiation on time scales]")
- 07:29, 29 March 2015 (diff | hist) . . (+60) . . Main Page (→$\Delta$-calculus)
- 23:46, 28 March 2015 (diff | hist) . . (+90) . . Real numbers
- 23:46, 28 March 2015 (diff | hist) . . (+573) . . Unilateral Laplace transform (→Table of Laplace transforms)
- 23:39, 28 March 2015 (diff | hist) . . (+32) . . Delta Wirtinger inequality
- 23:38, 28 March 2015 (diff | hist) . . (+32) . . Delta Tschebycheff inequality
- 23:38, 28 March 2015 (diff | hist) . . (+32) . . Delta Opial inequality
- 23:38, 28 March 2015 (diff | hist) . . (+32) . . Delta Minkowski inequality
- 23:38, 28 March 2015 (diff | hist) . . (+32) . . Delta Markov inequality
- 23:38, 28 March 2015 (diff | hist) . . (+32) . . Delta Lyapunov inequality
- 23:38, 28 March 2015 (diff | hist) . . (+32) . . Delta Jensen inequality
- 23:38, 28 March 2015 (diff | hist) . . (+32) . . Delta Hölder inequality
- 23:38, 28 March 2015 (diff | hist) . . (+32) . . Delta Gronwall inequality
- 23:37, 28 March 2015 (diff | hist) . . (+32) . . Delta Cauchy-Schwarz inequality
- 23:37, 28 March 2015 (diff | hist) . . (+32) . . Delta Bihari inequality
- 23:37, 28 March 2015 (diff | hist) . . (+30) . . Delta inequalities footer (current)
- 23:37, 28 March 2015 (diff | hist) . . (+681) . . N Delta inequalities footer (Created page with "<center><h2>$\Delta$-Inequalities</h2> <table><tr> <td> Bernoulli</td> <td> Bihari</td> <td>Delta Cauchy-Schwarz...")
- 23:34, 28 March 2015 (diff | hist) . . (+32) . . Delta Bernoulli inequality
- 23:32, 28 March 2015 (diff | hist) . . (+147) . . Real numbers
- 23:29, 28 March 2015 (diff | hist) . . (0) . . Main Page (→$\Delta$-calculus)
- 23:29, 28 March 2015 (diff | hist) . . (+432) . . Main Page (→$\Delta$-calculus)
- 23:29, 28 March 2015 (diff | hist) . . (0) . . m Delta Wirtinger inequality (Tom moved page Wirtinger inequality to Delta Wirtinger inequality)
- 23:29, 28 March 2015 (diff | hist) . . (+40) . . N Wirtinger inequality (Tom moved page Wirtinger inequality to Delta Wirtinger inequality) (current)
- 23:28, 28 March 2015 (diff | hist) . . (0) . . m Delta Tschebycheff inequality (Tom moved page Tschebycheff inequality to Delta Tschebycheff inequality)
- 23:28, 28 March 2015 (diff | hist) . . (+43) . . N Tschebycheff inequality (Tom moved page Tschebycheff inequality to Delta Tschebycheff inequality) (current)
- 23:28, 28 March 2015 (diff | hist) . . (0) . . m Delta Opial inequality (Tom moved page Opial inequality to Delta Opial inequality)
- 23:28, 28 March 2015 (diff | hist) . . (+36) . . N Opial inequality (Tom moved page Opial inequality to Delta Opial inequality) (current)
- 23:27, 28 March 2015 (diff | hist) . . (0) . . m Delta Minkowski inequality (Tom moved page Minkowski inequality to Delta Minkowski inequality)
- 23:27, 28 March 2015 (diff | hist) . . (+40) . . N Minkowski inequality (Tom moved page Minkowski inequality to Delta Minkowski inequality) (current)
- 23:27, 28 March 2015 (diff | hist) . . (0) . . m Delta Markov inequality (Tom moved page Markov inequality to Delta Markov inequality)
- 23:27, 28 March 2015 (diff | hist) . . (+37) . . N Markov inequality (Tom moved page Markov inequality to Delta Markov inequality) (current)
- 23:27, 28 March 2015 (diff | hist) . . (0) . . m Delta Lyapunov inequality (Tom moved page Lyapunov inequality to Delta Lyapunov inequality)
- 23:27, 28 March 2015 (diff | hist) . . (+39) . . N Lyapunov inequality (Tom moved page Lyapunov inequality to Delta Lyapunov inequality) (current)
- 23:26, 28 March 2015 (diff | hist) . . (0) . . m Delta Jensen inequality (Tom moved page Jensen inequality to Delta Jensen inequality)
- 23:26, 28 March 2015 (diff | hist) . . (+37) . . N Jensen inequality (Tom moved page Jensen inequality to Delta Jensen inequality) (current)
- 23:26, 28 March 2015 (diff | hist) . . (+122) . . Main Page (→$\Delta$-calculus)
- 23:26, 28 March 2015 (diff | hist) . . (0) . . m Delta Hölder inequality (Tom moved page Hölder inequality to Delta Hölder inequality)
- 23:26, 28 March 2015 (diff | hist) . . (+38) . . N Hölder inequality (Tom moved page Hölder inequality to Delta Hölder inequality) (current)
- 23:25, 28 March 2015 (diff | hist) . . (0) . . m Delta Gronwall inequality (Tom moved page Gronwall inequality to Delta Gronwall inequality)
- 23:25, 28 March 2015 (diff | hist) . . (+39) . . N Gronwall inequality (Tom moved page Gronwall inequality to Delta Gronwall inequality) (current)
- 23:25, 28 March 2015 (diff | hist) . . (+74) . . Main Page (→$\Delta$-calculus)
- 23:25, 28 March 2015 (diff | hist) . . (0) . . m Delta Cauchy-Schwarz inequality (Tom moved page Cauchy-Schwarz inequality to Delta Cauchy-Schwarz inequality)
- 23:25, 28 March 2015 (diff | hist) . . (+45) . . N Cauchy-Schwarz inequality (Tom moved page Cauchy-Schwarz inequality to Delta Cauchy-Schwarz inequality) (current)
- 23:25, 28 March 2015 (diff | hist) . . (+58) . . Main Page (→$\Delta$-calculus)
- 23:24, 28 March 2015 (diff | hist) . . (0) . . m Delta Bihari inequality (Tom moved page Bihari inequality to Delta Bihari inequality)
- 23:24, 28 March 2015 (diff | hist) . . (+37) . . N Bihari inequality (Tom moved page Bihari inequality to Delta Bihari inequality) (current)
- 23:24, 28 March 2015 (diff | hist) . . (-26) . . Main Page (→Inequalities)
- 21:43, 28 March 2015 (diff | hist) . . (+64) . . Main Page (→$\Delta$-calculus)
- 21:43, 28 March 2015 (diff | hist) . . (0) . . m Delta Bernoulli inequality (Tom moved page Bernoulli inequality to Delta Bernoulli inequality)
- 21:43, 28 March 2015 (diff | hist) . . (+40) . . N Bernoulli inequality (Tom moved page Bernoulli inequality to Delta Bernoulli inequality) (current)
- 12:36, 28 March 2015 (diff | hist) . . (+731) . . Diamond alpha Hölder inequality (current)
- 12:33, 28 March 2015 (diff | hist) . . (0) . . m Diamond alpha Hölder inequality (Tom moved page Diamond alpha holder inequality to Diamond alpha Hölder inequality)
- 12:33, 28 March 2015 (diff | hist) . . (+46) . . N Diamond alpha holder inequality (Tom moved page Diamond alpha holder inequality to Diamond alpha Hölder inequality) (current)
- 12:33, 28 March 2015 (diff | hist) . . (+1) . . N Diamond alpha Hölder inequality (Created page with "a")
- 12:32, 28 March 2015 (diff | hist) . . (+79) . . Main Page (→$\Diamond_{\alpha}$-calculus)
- 12:32, 28 March 2015 (diff | hist) . . (+51) . . Diamond alpha Minkowski's inequality
- 12:31, 28 March 2015 (diff | hist) . . (+600) . . N Diamond alpha Minkowski's inequality (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a time scale with $a,b \in \mathbb{T}$, $a<b$ and $p...")
- 12:29, 28 March 2015 (diff | hist) . . (+87) . . Main Page (→$\Diamond_{\alpha}$-calculus)
- 12:28, 28 March 2015 (diff | hist) . . (+582) . . N Diamond alpha Jensen's inequality (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> Let $\mathbb{T}$ be a time scale with $a,b \in \mathbb{T}$ with $a<b$ an...") (current)
- 12:25, 28 March 2015 (diff | hist) . . (+81) . . Main Page (→$\Diamond_{\alpha}$-calculus)
- 03:10, 28 March 2015 (diff | hist) . . (+6) . . Multiples of integers
- 03:10, 28 March 2015 (diff | hist) . . (+6) . . Closure of unit fractions
- 03:09, 28 March 2015 (diff | hist) . . (+44) . . Closure of unit fractions
- 03:08, 28 March 2015 (diff | hist) . . (0) . . N File:Closureunitfractionstimescale.png (current)
- 03:00, 28 March 2015 (diff | hist) . . (+27) . . Multiples of integers
- 02:59, 28 March 2015 (diff | hist) . . (0) . . N File:HZtime scale.png (current)
- 08:00, 23 March 2015 (diff | hist) . . (0) . . Nabla special functions footer (current)
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