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In this work, an analytical equilibrium solution to the Néel relaxation Fokker-Planck equation with a uniaxial anisotropy is presented. The solution is compared with a recently developed mathematical model that explains the spatial structure of the system function better than the Langevin function based model. The results presented show small relative errors on a large scale of typical particle parameters, so that both models can be considered approximately equivalent. The parameter choice for which both models diverge is outlined. The advantage of the proposed solution is its fast calculation in contrast to the numerical solution of the Fokker-Planck equation.