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In this note we construct a family of recurrence generated sigmoidal logistic functions based on the Verhulst logistic function.We prove estimates for the Hausdorff approximation of the Heaviside step function by means of this family. Numerical examples, illustrating our results are given.doi:10.11145/bmc.2016.12.177 fatcat:lmyclvspkbd3fjelecy63czxpe