John D. Cook • 5/31/2026

Another Gaussian approximation

This article discusses an alternative Gaussian approximation using the function (1 + cos(sin(x) + x))/2, which matches the power series for exp(-x²) with an error on the order of x⁶/240. The author examines the tension between the theoretical error bound and the actual error at x=4, noting that the alternating series theorem does not apply because the series terms are not decreasing. The post provides insights into approximation methods and series behavior, relevant to mathematical computing and numerical analysis.

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#Power Series #Alternating Series #Gaussian Approximation