>

>	restart;with(plots):

Warning, the name changecoords has been redefined

>	bool:=proc(expression) piecewise(expression,1,0); end:

>	LegendreQ_demi:=(n,z)-> (sqrt(Pi)/exp((n+1/2)*(arccosh(z)+ln(2)))/GAMMA(n+1))* hypergeom([n+1/2,1/2],[n+1],exp(-2*arccosh(z)));

>	f:=(v,x,y)->(Re(LegendreQ_demi(v,x+I*y)),Im(LegendreQ_demi(v,x+I*y))): g:=(v,p,x,y)->(Re(LegendreP(v,p,x+I*y)),Im(LegendreP(v,p,x+I*y))):

>	m:=(F,v,p,x,y)->sqrt(F(v,p,x,y)[1]^2+F(v,p,x,y)[2]^2): phi:=(F,v,p,x,y)->arctan(F(v,p,x,y)[2]/F(v,p,x,y)[1])+bool(F(v,p,x,y)[2]<0)*Pi: Kx:=-10..10; Ky:=-10..10;Kz:=-200..200;

>	animate3d([x,y,m(f,p+0.5,0,x,y)],x=Kx,y=Ky,p=0..8,frames=10,                               axes=BOXED,labels=["x","y","mod(f)"]);

Animation : (x, y, module) des fonctions de Legendre de 2nde espèce ( n  = 5, 0 <  m < 8)

>

nu:=40:

>	plot3d([x,y,m(g,0.5,0,x,y)],x=Kx,y=Ky,                               axes=BOXED,labels=["x","y","mod(f)"],grid=[nu,nu]);

>

>

nu:=40:

>	plot3d([x,y,m(f,1,0,x,y)],x=Kx,y=Ky,                              axes=BOXED,labels=["x","y","mod(f)"],grid=[nu,nu]);