A pair of optimal inequalities related to the error function

1997/11/11 by Mary Beth Ruskai, M. Beth Ruskai, Ruskai, M. Beth +3
Decision Sciences · Mathematics · #33B10 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Mathematical functions and polynomials #Probabilistic and Robust Engineering Design #math.FA #msc:33B10

paper · pdf · doi:10.48550/arxiv.math/9711207

arxiv created 1997/11/11 · openalex publication_date 1997/11/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Error Function V(x) ≡ √π e^x2 [1 - \hboxerf(x)]
= ∫₀^∞ \frac e^-u √(x² + u) du = 2 e^x2∫_x^∞ e^-t2 dt arises in many contexts, from probability to mathematical physics. We give estimates for the Error Function from above and below which are optimal within a certain class of functions.

Citations

• Confidence regions for means of multivariate normal distributions and a non-symmetric correlation inequality for gaussian measure

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