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Description

Legendre Polynomial of cos(θ) with l=2, m=0

Date

24 May 2007

Source

Own work

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Author

Inductiveload

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(Reusing this file)

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Category:Self-published work#Legendre(2,0)%20Cos(th).svg Category:PD-self#Legendre(2,0)%20Cos(th).svg

Mathematical Function Plot
Description	Legendre Polynomial of cos(θ) with 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	$\cos \theta =\pm {\frac {1}{\sqrt {3}}}$

Category:Spherical harmonics

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File:Legendre(2,0) Cos(th).svg