![[Maple OLE 2.0 Object]](images/legendre4_harmoniques1.gif)
Harmoniques sphériques
| > | restart: with(plots): |
Warning, the name changecoords has been redefined
| > | f:=u->sqrt(u): |
| > | kn:=20:km:=20: |
| > | for n from 0 to kn do c[n]:=evalf((n+1/2)*int(f(u)*LegendreP(n,u), u=-1..1)); a[n]:=1: od: |
| > | vv:=(m,r,u)->sum('c[k]*r^k*LegendreP(k,m,u)','k'=0..kn); |
| > |
![vv := proc (m, r, u) options operator, arrow; sum('c[k]*r^k*LegendreP(k,m,u)',('k') = 0 .. kn) end proc](images/legendre4_harmoniques2.gif)
| > | plot([Re(vv(0,0.5,u)),u,u=0..2*Pi],coords=polar); |
![[Maple Plot]](images/legendre4_harmoniques3.gif)
| > | V:=(r,u,v)->sum('a[j]*exp(I*j*v)*vv(j,r,u)','k'=0..km); |
![V := proc (r, u, v) options operator, arrow; sum('a[j]*exp(j*v*I)*vv(j,r,u)',('k') = 0 .. km) end proc](images/legendre4_harmoniques4.gif)
| > |
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