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Calculating moments of exponential densities using differential algebraic equations

This article introduces an efficient approach for calculating the moments of exponential densities. Usually, the desired moments are obtained by means of numerical integration, which is impractical due to its computational complexity and the underlying infinite integration intervals. The new approach relies on an exact conversion of these integrals into a system of ordinary differential equations with algebraic constraints. The desired moments are then obtained by solving this system of differential algebraic equations over a finite "time" interval. The resulting procedure is simple to implement and typically reduces the computational burden by one order of magnitude.