The orthogonality of spherical harmonics of different degree follows from the fact that spherical harmonics are eigenfunctions of the spherical Laplacian. Since the spherical Laplacian is self-adjoint the orthogonality follows.
The orthogonality of spherical harmonics of different degree follows from the fact that spherical harmonics are eigenfunctions of the spherical Laplacian. Since the spherical Laplacian is self-adjoint the orthogonality follows.