  The method of moments is developed and employed to analyze the equilibrium
correlation functions of the magnetization of ferromagnetic nanoparticles in
the case of inertial magnetization dynamics. The method is based on the Taylor
series expansion of the correlation functions and the estimation of the
expansion coefficients. This method significantly reduces the complexity of
analysis of equilibrium correlation functions. Analytical expressions are
derived for the first three coefficients for the longitudinal and transverse
correlation functions for the uniaxial magnetocrystalline anisotropy of
ferromagnetic nanoparticles with a longitudinal magnetic field. The limiting
cases of very strong and negligibly weak external longitudinal fields are
considered. The Gordon sum rule for inertial magnetization dynamics is
discussed. In addition, we show that finite analytic series can be used as a
simple and satisfactory approximation for the numerical calculation of
correlation functions at short times.
