User:Inductiveload/Mathematical Function

{| class="wikitable"
!colspan=2|[[Image:Icon Mathematical Plot.svg]]      Mathematical Function Plot
|-
!Description
|[[w:Legendre Polynomial|Legendre Polynomial]], l=2, m=0
|-
!Equation
|<math>Y_0^2 \left(\theta \right)=\frac{1}{2} \left( 3 \cos^2 \left(\theta \right) - 1 \right)</math>
|-
!Co-ordinate System
|[[w:Cartesian|Cartesian]]
|-
!X Range
|0 .. 2π
|-
!Y Range
| -1 .. 1
|-
|colspan=2| 
|-
!colspan=2|Points of Interest in this Range
|-
!Maxima
| <math>\left( 0,1 \right)\,,</math> <math>\left( \pi,1 \right)\,,</math> <math>\left(2\pi,1 \right)\,</math>
|-
!Minima
| <math>\left( \frac{\pi}{2},-\frac{1}{2} \right),</math> <math>\left( \frac{3\pi}{2},-\frac{1}{2} \right)</math>
|-
!Roots
| <math>\cos \theta = \pm \frac{1}{\sqrt{3}}</math>

|}

Produces:

Mathematical Function Plot
Description	Legendre Polynomial, l=2, m=0
Equation	$Y_{0}^{2}\left(\theta \right)={\frac {1}{2}}\left(3\cos ^{2}\left(\theta \right)-1\right)$
Co-ordinate System	Cartesian
X Range	0 .. 2π
Y Range	-1 .. 1
Points of Interest in this Range
Maxima	$\left(0,1\right)\,,$ $\left(\pi ,1\right)\,,$ $\left(2\pi ,1\right)\,$
Minima	$\left({\frac {\pi }{2}},-{\frac {1}{2}}\right),$ $\left({\frac {3\pi }{2}},-{\frac {1}{2}}\right)$
Roots	$\cos \theta =\pm {\frac {1}{\sqrt {3}}}$

Formula Box

::{|style=" border: solid 2px #D6D6FF; padding: 1em;" valign="top" 
|align="left"|<math>R_L=R_s \,</math>
|}

Produces:

$R_{L}=R_{s}\,$

Antialiasing Code

{|style=" border: solid 2px #D6D6FF; ;" valign="top"; width=75% align=center
|[[image:Antialias Icon.svg|50px]]
|This uses Chris Hill's antialiasing code to average pixels and produce a less jagged image. The original code can be found [http://members.wri.com/jeffb/visualization/aa.shtml here].
|[[image:Icon Mathematical Plot.svg|50px]]
|}

Produces:

This uses Chris Hill's antialiasing code to average pixels and produce a less jagged image. The original code can be found here.

Processing Time Warning

{|style=" border: solid 2px #BF0C1D; ;" valign="top"; width=75% align=center
|[[Image:Nuvola apps important.svg|50px]]
|Please be aware that at the time of uploading (~~~~~), this code may take a significant amount of time to execute on a consumer-level computer.
|[[Image:Integrated circuit icon.svg|50px]]
|}

Produces:

Please be aware that at the time of uploading (21:19, 13 June 2007 (UTC)), this code may take a significant amount of time to execute on a consumer-level computer.