legendre1.mws

>   

>    restart;with(plots): 

Warning, the name changecoords has been redefined

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

     

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

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

>    animate3d([x,y,f(v,x,y)[1]],x=Kx,y=Ky,v=0..8,frames=20,view=Kz,
                          axes=BOXED,labels=["x","y","Re(f)"]);

[Maple Plot]

Animation : partie réelle des polynômes de Legendre (0 < n < 8)

>    animate3d([x,y,f(v,x,y)[2]],x=Kx,y=Ky,v=0..8,frames=20,view=Kz,
                           axes=BOXED,labels=["x","y","Im(f)"]);

>   

[Maple Plot]

Animation : partie imaginaire des polynômes de Legendre (0 < n < 8)

>    animate3d([x,f(v,x,y)[1],f(v,x,y)[2]],x=Kx,y=Ky,v=0..8,frames=20,view=Kz,axes=BOXED,labels=["x","Re(f)","Im(f)"]);

[Maple Plot]

Animation : (x, réelle, imaginaire) des polynômes de Legendre (0 < n < 8)

>    animate3d([y,f(v,x,y)[1],f(v,x,y)[2]],x=Kx,y=Ky,v=0..8,frames=20,view=Kz,
                                     axes=BOXED,labels=["y","Re(f)","Im(f)"]);

[Maple Plot]

Animation : (y, réelle, imaginaire) des polynômes de Legendre (0 < n < 8)

>    animate3d([x,y,m(v,x,y)],x=Kx,y=Ky,v=0..8,frames=20,view=Kz,
                              axes=BOXED,labels=["x","y","mod(f)"]);

[Maple Plot]

Animation : (x, y, module) des polynômes de Legendre (0 < n < 8)

>    plot3d([x,y,phi(3,x,y)],x=Kx,y=Ky,axes=BOXED,labels=["x","y","arg(f)"], grid=[50,50]);

[Maple Plot]

(x, y, argument) du polynôme de Legendre ( n =  8)

>     plot([seq(LegendreP(i,x),i=0..10 )],x=-1..1);

[Maple Plot]

(x, Pn(x)), polynômes de Legendre (0 < n < 10)

>    p := seq(
        plot(LegendreP(i/10,x),x=-1..1,
        color=COLOR(HUE, i/100)),
        i=0..100
         ):

>    display([p],insequence=true);

>   

[Maple Plot]

Animation : (x, Pn(x)) de 100 polynômes de Legendre (0 < n < 10)

>    p := seq(
        plot(LegendreP(i/10,cos(t)),t=-Pi..Pi,
        color=COLOR(HUE, i/100)),
        i=0..100
         ):

>    display([p],insequence=true);

[Maple Plot]

Animation : (t, Pn(cos(t))) de 100 polynômes de Legendre (0 < n < 10)

>   

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