... Consequently, it is inappropriate to expand and in ordinary spherical harmonics. The proper expansion expresses both and simultaneously in terms of a particular order of generalized spherical harmonics. ... Generalized spherical harmonics start at , and for each , . ... Generalized spherical harmonics obey a sum rule analogous to a familiar one for ordinary spherical harmonics, but it includes an explicit phase factor which depends on the orientation of the two lines of sight. ...