# β

{| class=prettytable
!colspan=2|[[Image:Icon Mathematical Plot.svg]]      Mathematical Function Plot
|-
!Description
|[[w:Legendre Polynomial|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
|[[w:Cartesian|Cartesian]]
|-
!X Range
|0 .. 2π
|-
!Y Range
| -1 .. 1
|-
|colspan=2|
|-
!colspan=2|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
| $\cos \theta = \pm \frac{1}{\sqrt{3}}$

|}


Produces:

Mathematical Function Plot
Description Legendre Polynomial, l=2, m=0
Equation ${\displaystyle Y_{0}^{2}\left(\theta \right)={\frac {1}{2}}\left(3\cos ^{2}\left(\theta \right)-1\right)}$
Co-ordinate System Cartesian
X Range 0 .. 2π
Y Range -1 .. 1

Points of Interest in this Range
Maxima ${\displaystyle \left(0,1\right)\,,}$ ${\displaystyle \left(\pi ,1\right)\,,}$ ${\displaystyle \left(2\pi ,1\right)\,}$
Minima ${\displaystyle \left({\frac {\pi }{2}},-{\frac {1}{2}}\right),}$ ${\displaystyle \left({\frac {3\pi }{2}},-{\frac {1}{2}}\right)}$
Roots ${\displaystyle \cos \theta =\pm {\frac {1}{\sqrt {3}}}}$

## Formula BoxEdit

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


Produces:

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

## Antialiasing CodeEdit

{|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 WarningEdit

{|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.