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This article presents a compact analytic approximation to the solution of a nonlinear partial differential equation of the diffusion type by using Bürmann's theorem. Expanding an analytic function in powers of its derivative is shown to be a useful approach for solutions satisfying an integral relation, such as the error function and the heat integral for nonlinear heat transfer. Based on this approach, series expansions for solutions of nonlinear equations are constructed. The convergence of adoi:10.3888/tmj.16-11 fatcat:fncoivjbgrh7vac7rxjdt7pkkm