  Series representations consisting of spherical harmonics are obtained for
characteristic exponents and probability density functions of multivariate
stable distributions under various conditions. A esult potentially applicable
in a practical setting is that for any distribution with stability index not
equal to 1 and with a polynomial spectral spherical density, the series
representation converges absolutely with all terms being calculable in closed
form. Asymptotic expansions consisting of spherical harmonics are also
considered for probability density functions.
