The eigenfunctions of (30.2.1) that correspond to the eigenvalues are denoted by , . They are normalized by the condition
the sign of being when is even, and the sign of being when is odd.
When is the prolate angular spheroidal wave function, and when is the oblate angular spheroidal wave function. If , reduces to the Ferrers function :
has exactly zeros in the interval .
If is mean-square integrable on , then formally