x[theta_, phi_] := Cos[phi] Sin[theta] ; y[theta_, phi_] := Sin[phi] Sin[theta] ; z[theta_, phi_] := Cos[theta];
findmaxSphericalharmonic[l_, m_] := First[ NMaximize[Abs[SphericalHarmonicY[l, m, theta, phi]] , {theta, phi}] ] ;