legendre6_associees2.mws

>   

>    restart;with(plots): 

Warning, the name changecoords has been redefined

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

     

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

>    m:=(v,p,x,y)->sqrt(f(v,p,x,y)[1]^2+f(v,p,x,y)[2]^2):
phi:=(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:=-1..1; Ky:=-1..1;Kz:=-200..200;

>    animate3d([x,y,m(5,p,x,y)],x=Kx,y=Ky,p=0..8,frames=30,view=0..500,
                              axes=BOXED,labels=["x","y","mod(f)"]);

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

[Maple Plot]

>    plot3d([x,y,m(5,5,x,y)],x=Kx,y=Ky,view=0..1500,
                              axes=BOXED,labels=["x","y","mod(f)"]);

[Maple Plot]

Attention, Maple semble coincer sur les m  < 0...

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Math rendered by WebEQ