In the post-Newtonian expansion, the parameter
is assumed to
be small. Then, it is straightforward to obtain a spheroidal
harmonic
of
spin-weight
and
its eigenvalue
perturbatively by the standard method [46, 58
, 52
].
It is also possible to obtain the spheroidal
harmonics by expansion in terms of the Jacobi functions [21]. In
this method, if we calculate numerically, we can obtain them and
their eigenvalues for an arbitrary value of .
Here we only show an analytic formula for the
eigenvalue
accurate to
, which is needed for the calculation of the radial
functions. It is given by