matlab - Unable to plot a surface defined implicitly -
i have following function, bit complicated:
x1=function[{r,\[theta],l},4re[(n[integrate[e^(-(r^2+r^2)+2 r l/r) (r+i r)^(2 l) (laguerrel[1/2 (-l+n),l,(r^2+r^2)])^2 ,{r,-\[infinity],\[infinity]}]])]];
where function constant in [theta], function defines surface (more or less cylindrical) through equation x1(r, [theta], l)=0.08, let's say.
problem i'm unable draw neither commands: contourplot3d, listcontourplot3d of mathematica, in matlab not able deal laguerre generalized polynomials plot isosurface :_(
assuming n defines order of laguerre polynomials , r length of 3-dimensional vector (x,y,z) contour plots equation.
to make calculations little more efficient defined integral memo function:
fx1nl[n_, l_] := fx1nl[n, l] = 4 re[(n[integrate[ e^(-(r^2 + r^2) + 2 r l/r) (r + r)^(2 l) (laguerrel[ 1/2 (-l + n), l, (r^2 + r^2)])^2, {r, -\[infinity], \[infinity]}]])]
(i don't know how incorporate dependence on r in definition have following hack instead:
fx1[rp_, n_, l_] := fx1nl[n, l] /. r -> rp
then can go ahead with
contourplot3d[ fx1[sqrt[x^2 + y^2 + z^2], 1, 1] == 0.08, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}]
... instance.
i not having luck evaluating function other values of n , l maybe need work integrals out before going there.
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