Expansion coefficients for the Klein-Nishina differential cross section are presented for 17 energies in the range 0.1 to 12.0 MeV. The maximum order of these coefficients for the higher photon energies is L = 35. An interpolation procedure for the generation of expansion coefficients at additional energies is also presented. A study is made of the errors introduced in the Klein-Nishina cross section when finite order polynomial approximations are used. The error investigation includes average-weighted percent error, local percent error at θ = 0, forward-weighted percent error, and angular regions in which the expanded differential cross section is negative. The average-weighted percent error is found to be indicative of all other errors. Results indicate that cross-section errors at various energies and orders of expansion may be readily predicted. Several methods are introduced for determining a suitable degree of expansion to ensure accuracy of the finite order expansion of the Klein-Nishina differential cross section.