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spherical_harmonic

? spherical_harmonic;

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spherical_harmonic

spherical_harmonic(4,...

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spherical_harmonic

? spherical_harmonic;

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spherical_harmonic

spherical_harmonic(1,...

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spherical_harmonic

spherical_harmonic(0,...

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spherical_harmonic

spherical_harmonic (1...

Calculate

spherical_harmonic

spherical_harmonic(1,...

Calculate

spherical_harmonic

? spherical_harmonic;

Calculate

spherical_harmonic

spherical_harmonic(1,...

Calculate

spherical_harmonic

spherical_harmonic(1,...

Calculate

spherical_harmonic

Run Example
(%i1)load(orthopoly);
(%o1)       /usr/share/maxima/5.21.1/share/orthopoly/orthopoly.lisp
(%i2) tubo:spherical_harmonic(2,0,theta,phi);
                                                             2
                                           3 (1 - cos(theta))
           sqrt(5) (- 3 (1 - cos(theta)) + ------------------- + 1)
                                                    2
(%o2)      --------------------------------------------------------
                                 2 sqrt(%pi)
(%i3) plot3d(tubo^2,[theta,0,%pi],[phi,0,2*%pi],[transform_xy,spherical_to_xyz],[grid,30,60]);
plotplot3d(tubo^2,[theta,0,%pi],[phi,0,2*%pi],[transform_xy,spherical_to_xyz],[grid,30,60]);
Run Example
load(orthopoly);
(%o1)       /usr/share/maxima/5.21.1/share/orthopoly/orthopoly.lisp
(%i2) tubo:spherical_harmonic(1,1,theta,phi);
                                    %i phi
                          sqrt(3) %e       sin(theta)
(%o2)                     ---------------------------
                                 3/2
                                2    sqrt(%pi)
(%i3) plot3d(tubo,[theta,0,%pi],[phi,0,2*%pi],[transform_xy,spherical_to_xyz],[grid,30,60]);
plotplot3d(tubo,[theta,0,%pi],[phi,0,2*%pi],[transform_xy,spherical_to_xyz],[grid,30,60]);
Run Example
f(x,y):=ln(1+x^2+2*x+y^2);
                                          2          2
(%o1)                  f(x, y) := ln(1 + x  + 2 x + y )
(%i2) diff(f(x,y));
       d       2    2                        d       2    2
(%o2) (-- (ln(y  + x  + 2 x + 1))) del(y) + (-- (ln(y  + x  + 2 x + 1))) del(x)
       dy                                    dx
(%i3) f(x,y):=x*sin(y);
(%o3)                         f(x, y) := x sin(y)
(%i4) gradiente:jacobian([f(x,y)],[x,y]);
(%o4)                        [ sin(y)  x cos(y) ]
(%i5) matrizhess:hessian(f(x,y),[x,y]);
                            [   0       cos(y)   ]
(%o5)                       [                    ]
                            [ cos(y)  - x sin(y) ]
(%i6) spherical_harmonic (n, m, x, y);
                                    m
(%o6)                              Y (x, y)
                                    n
(%i7) 

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