Last modified on 26 August 2007, at 14:09

User:Inductiveload/Mathematical Function

{| class=prettytable
!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:

Icon Mathematical Plot.svg      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 BoxEdit

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

Produces:

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:

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

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:

Nuvola apps important.svg 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. Integrated circuit icon.svg