@Markiyan Hirnyk So the code I posted isn't commented at all. If you would like I could add comments to make it more readable?

@Markiyan Hirnyk So the code I posted isn't commented at all. If you would like I could add comments to make it more readable?

AlternativeRshRotTes.mw....here's the link.

AlternativeRshRotTes.mw....here's the link.

So, the identities stated in the correction following my question:

           Re( SphericalY(2*l, -2*l, theta, phi) )  = Re ( SphericalY(2*l, 2*l, theta, phi) ), and 

           abs( Img( SphericalY(2*l, -2*l, theta, phi) ) ) = abs( Img( SphericalY(2*l, 2*l, theta, phi) ) ).

These identies follow from the definition of SphericalY. Typing something like 

                     convert(SphericalY(l, m, t, p), LegendreP);

gives a clear symbolic formula, from which the identies follow. Now, as far as making Maple prove an identity, I'm not sure. Though, you can use the following code to check equality of formulas:

                     is(SphericalY(lambda, -mu, theta, phi) = SphericalY(lambda, mu, theta, phi));

So, the identities stated in the correction following my question:

           Re( SphericalY(2*l, -2*l, theta, phi) )  = Re ( SphericalY(2*l, 2*l, theta, phi) ), and 

           abs( Img( SphericalY(2*l, -2*l, theta, phi) ) ) = abs( Img( SphericalY(2*l, 2*l, theta, phi) ) ).

These identies follow from the definition of SphericalY. Typing something like 

                     convert(SphericalY(l, m, t, p), LegendreP);

gives a clear symbolic formula, from which the identies follow. Now, as far as making Maple prove an identity, I'm not sure. Though, you can use the following code to check equality of formulas:

                     is(SphericalY(lambda, -mu, theta, phi) = SphericalY(lambda, mu, theta, phi));

My apologies. What I meant to write was,

Re( SphericalY(2*l, -2*l, theta, phi) )  = Re ( SphericalY(2*l, 2*l, theta, phi) ), and 

abs( Img( SphericalY(2*l, -2*l, theta, phi) ) ) = abs( Img( SphericalY(2*l, 2*l, theta, phi) ) )

is true in Maple 13, but doesn't seem to be the case in Maple 14. 

Thanks so much for your answer Joe. Does this scheme also work for a list of points and function values? Your solution uses a function definition, which I don't have. What I do have are points on S2 and the values in R, which those points map to. I guess what I'm looking for is function or some way of taking my list {point*f(point)} and triangulating this list, like Voronoi diagrams.

Let me know if you have any ideas:)

Thanks so much for your answer Joe. Does this scheme also work for a list of points and function values? Your solution uses a function definition, which I don't have. What I do have are points on S2 and the values in R, which those points map to. I guess what I'm looking for is function or some way of taking my list {point*f(point)} and triangulating this list, like Voronoi diagrams.

Let me know if you have any ideas:)