Integrals Related to the Error Function
نویسندگان
چکیده
منابع مشابه
A Pair of Optimal Inequalities Related to the Error Function
The function V (x) ≡ √ πe x 2 [1 − erf(x)] (1) = ∞ 0 e −u √ x 2 + u du = 2e x 2 ∞ x e −t 2 dt arises in many contexts, from probability to mathematical physics, and satisi-fies the differential equation V ′ (x) = 2xV (x) − 2 with V (0) = √ π. (2) In this note, we restrict attention to x ≥ 0, in which case 0 < V (x) < 1/x and V (x) is decreasing. For x ≥ 0 we show that g π (x) ≤ V (x) < g 4 (x) (3)
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ژورنال
عنوان ژورنال: Technometrics
سال: 2020
ISSN: 0040-1706,1537-2723
DOI: 10.1080/00401706.2020.1825632