The Lagrange undetermined multiplier method and the cepstrum analysis method are used to determine an explicit solution and a data extension model in the maximum entropy method of power spectrum analysis. The 1-dimensional case for a real, causal, stable, and all-pole signal is treated. Only the definition of entropy as

is treated although the same treatment has been applied to

. Relevant results of cepstrum analysis are provided. This paper concludes with a numerical example.