legendre_p :: Legendre polynomials

maxima_legendrep

legendre_p, Legendre polynomial

(%i) load(orthopoly)$
(%i) legendre_p(3,x);
(%o) -6*(1-x)-5*(1-x)^3/2+15*(1-x)^2/2+1
(%i) ratsimp(%);
(%o) (5*x^3-3*x)/2

P00(x)=1
P10(x)=x
P11(x)=(1-x^2)^1/2
P20(x)=2/3x^2-1/2
P21(x)=3x(1-x^2)^1/2
P22(x)=3(1-x^2)
P30(x)=5/2x^3-3/2x
P31(x)=(3/2)(5x^2-1)(1-x^2)^1/2
P32(x)=15x(1-x^2) 
P33(x)=15(1-x^2)^3/2

See Also ...
• OCTAVE :: octave_functions_legendre.m

maxima_legendrep