Format notes

This is a list of common code templates and styles we use at timescalewiki.

Theorem/proof box template

The code

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
<strong>THEOREM/LEMMA/PROPOSITION:</strong> STATEMENT OF THEOREM
<div class="mw-collapsible-content">
<strong>Proof:</strong> proof goes here █ 
</div>
</div>

creates

THEOREM/LEMMA/PROPOSITION: STATEMENT OF THEOREM

Proof: proof goes here █

Generic list of time scales

The code

{| class="wikitable"
|+Time Scale foo Functions
|-
|$\mathbb{T}$
|
|-
|[[Real_numbers | $\mathbb{R}$]]
|$foo(t)=  $
|-
|[[Integers | $\mathbb{Z}$]]
|$foo(t) = $
|-
|[[Multiples_of_integers | $h\mathbb{Z}$]]
| $foo(t) = $
|-
| [[Square_integers | $\mathbb{Z}^2$]]
| $foo(t) = $
|-
|[[Quantum_q_greater_than_1 | $\overline{q^{\mathbb{Z}}}, q > 1$]]
| $foo(t) = $
|-
|[[Quantum_q_less_than_1 | $\overline{q^{\mathbb{Z}}}, q < 1$]]
| $foo(t) =$
|-
|[[Harmonic_numbers | $\mathbb{H}$]]
|$foo(t) = $
|}

generates

Time Scale foo Functions

$\mathbb{T}$
$\mathbb{R}$	$foo(t)= $
$\mathbb{Z}$	$foo(t) = $
$h\mathbb{Z}$	$foo(t) = $
$\mathbb{Z}^2$	$foo(t) = $
$\overline{q^{\mathbb{Z}}}, q > 1$	$foo(t) = $
$\overline{q^{\mathbb{Z}}}, q < 1$	$foo(t) =$
$\mathbb{H}$	$foo(t) = $

General format for time scale pages

$\mathbb{T}=TIMESCALESYMBOL$

Forward jump:	$\sigma(t)=$	derivation
Forward graininess:	$\mu(t)=$	derivation
Backward jump:	$\rho(t)=$	derivation
Backward graininess:	$\nu(t)=$	derivation
$\Delta$-derivative	$f^{\Delta}(t)=$	derivation
$\nabla$-derivative	$f^{\nabla}(t)=$	derivation
$\Delta$-integral	$\displaystyle\int_s^t f(\tau) \Delta \tau=$	derivation
$\nabla$-integral	$\displaystyle\int_s^t f(\tau) \nabla \tau=$	derivation
$h_k(t,s)$	$h_k(t,s)=$	derivation
$\hat{h}_k(t,s)$	$\hat{h}_k(t,s)=$	derivation
$g_k(t,s)$	$g_k(t,s)=$	derivation
$\hat{g}_k(t,s)$	$\hat{g}_k(t,s)=$	derivation
$e_p(t,s)$	$e_p(t,s)=$	derivation
$\hat{e}_p(t,s)$	$\hat{e}_p(t,s)=$	derivation
Gaussian bell	$\mathbf{E}(t)=$	derivation
$\mathrm{sin}_p(t,s)=$	$\sin_p(t,s)=$	derivation
$\mathrm{\sin}_1(t,s)$	$\sin_1(t,s)=$	derivation
$\widehat{\sin}_p(t,s)$	$\widehat{\sin}_p(t,s)=$	derivation
$\mathrm{\cos}_p(t,s)$	$\cos_p(t,s)=$	derivation
$\mathrm{\cos}_1(t,s)$	$\cos_1(t,s)=$	derivation
$\widehat{\cos}_p(t,s)$	$\widehat{\cos}_p(t,s)=$	derivation
$\sinh_p(t,s)$	$\sinh_p(t,s)=$	derivation
$\widehat{\sinh}_p(t,s)$	$\widehat{\sinh}_p(t,s)=$	derivation
$\cosh_p(t,s)$	$\cosh_p(t,s)=$	derivation
$\widehat{\cosh}_p(t,s)$	$\widehat{\cosh}_p(t,s)=$	derivation
Gamma function	$\Gamma_{TIMESCALESYMBOL}(x,s)=$	derivation
Euler-Cauchy logarithm	$L(t,s)=$	derivation
Bohner logarithm	$L_p(t,s)=$	derivation
Jackson logarithm	$\log_{TIMESCALESYMBOL} g(t)=$	derivation
Mozyrska-Torres logarithm	$L_{TIMESCALESYMBOL}(t)=$	derivation
Laplace transform	$\mathscr{L}_{TIMESCALESYMBOL}\{f\}(z;s)=$	derivation
Hilger circle		derivation

Categories

[[Category:Plot]]
[[Category:TimeScaleDeltaExponential]]
[[Category:TimeScale:Integers]]