function y = legendre0(x)
y = ones(x);
endfunction;

function y = legendre1(x)
y = x;
endfunction;

function y = legendre2(x)
y = (3*x.^2-1)./2;
endfunction;

function y = legendre3(x)
y = (5*x.^3-3*x)./2;
endfunction;

function y = legendre4(x)
y = (35*x.^4-30*x^2+3)./8;
endfunction;

function y = legendre5(x)
y = (63*x.^5-70*x^3+15*x)./8;
endfunction;

scf(0);
clf();
t=-1:0.01:1;
plot(t,legendre0(t),'k:');
plot(t,legendre1(t),'k-');
plot(t,legendre2(t),'b:');
plot(t,legendre3(t),'b-');
plot(t,legendre4(t),'r:');
plot(t,legendre5(t),'r-');
xtitle('Legendre Polynominals 0 to 5','x','P_n(x)');

scf(1);
clf()
phi=0:0.01:%pi;
t=cos(phi);
plot(phi,legendre0(t),'k:');
plot(phi,legendre1(t),'k-');
plot(phi,legendre2(t),'b:');
plot(phi,legendre3(t),'b-');
plot(phi,legendre4(t),'r:');
plot(phi,legendre5(t),'r-');
xtitle('Legendre Polynominals 0 to 5','phi','P_n(cos(phi))');