I want to solve this integral
Integrate[
SphericalHarmonicY[l, m, o, p]*SphericalHarmonicY[l, n, o, p]*
SphericalHarmonicY[l, i, o, p]*SphericalHarmonicY[l, j, o, p], {o,
0, Pi}, {p, 0, 2 Pi}]
but mathematica doesn't give me an answer. I also tried: (simplified in terms of Legendre polynomials and exponential)
Integrate[
Integrate[
LegendreP[l, m, o]*LegendreP[l, n, o]*LegendreP[l, i, o]*
LegendreP[l, j, o]*Exp[I*(m - n - i + j)], {o, 0, Pi}], {p, 0,
2 Pi}]
But still no helpful answer, can anybody help me with this?