Expressions for point source Green's functions are developed which mathematically describe monoenergetic, neutral particle transport in uniform, unbounded media with particle absorption and azimuthally symmetric scattering of finite-degree polar angle anisotropy. The method of development follows closely the plane source superposition technique of Fano, Spencer, and Berger with the extension of explicit formulation of the relevant plane symmetry functions. Some limit properties of the derived Green's function are considered.