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Characterization of the Central Limit Theorem by the Burmann Power Series

Richard F. Patterson, Pali Sen


The goal of this paper is to present a summability method for Burmann power series distribution that exclusively has been studied for its discrete properties. Here we extend the properties for discrete as well as continuous parameters and derive the conditions for the series to converge to a Gaussian distribution with mean zero and a finite variance. Based on the central limit theorem for the summability methods. We consider weighted sums of the Burmann function with iid random variables and combine distribution theory with the summability theory The series has been studied for within boundary points and outside the boundary points for tail convergence. Two special functions of weights originating from classical analysis are discussed.


Normal Distribution, Finite Moments Central limit Theorem, Burmann Series, Independent Identically Distributed Random Variables, Euler sum, Borel sum

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