LegendreP[3,Cos[θ]]

LegendreP[1,x]

LegendreP[2,x]

LegendreP[3,x]

LegendreP[4,x]

l=20
y=LegendreP[l,x]
Simplify[(1-(x^2))D[y,{x,2}]-2x D[y,x]+l(l+1)y]

lista=Table[LegendreP[i,x],{i,1,3}]

Plot[lista,{x,-1,1},PlotRange->All]

matriz=Table[i j,{i,1,2},{j,1,2}]
MatrixForm[matriz]

Integrate[LegendreP[2,x]LegendreP[2,x],{x,-1,1}]

Plot[LegendreP[21,Cos[θ]],{θ,0,π}]

D[D[x (z^2),{x,1}],{z,2}]

n=2
Expand[(1/((2^n)n!))D[((((x^2)-1))^n),{x,n}]]
LegendreP[n,x]

Simplify[((Sin[x])^2)+((Cos[x])^2)]