SphericalHarmonicY[l,m,pi/2,0] is supposed to be equal to SphericalHarmonicY[l,m,-pi/2,0] as they both are analytically written in terms of LegendreP[l,m,0] (as Cos[ +- pi/2 ] = 0). But they give out different answers. Try for example SphericalHarmonicY[1,1,pi/2,0 and the same with -pi/2.
It does this because it changes the Ylm's in terms of trig functions.(see documentation center's first example for SphericalHarmonicY)
Just wanted to confirm it. I thing using Abs will overcome this problem.
So does anyone agree?