The Debye series is developed for scattering of light by a homogeneous nonspherical particle to interpret the angular dependence of the scattered intensity in terms of various physical processes. In contrast to the previously developed Debye series for several regularly shaped particles that mirror the orthogonal curvilinear coordinate system where the variable-separation method can be applied, we develop and verify the Debye series in a coordinate-independent way using the extended boundary condition method. Verification computations are made for an oblate spheroidal water droplet of equivalent-volume sphere radius 10 mu m.