Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 2, pp. 367-371
Citer cet article
P. Kouznetzoff; A. S. Yudina. Some Asymptotic Expansions for an Incomplete Probability Integral. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 2, pp. 367-371. http://geodesic.mathdoc.fr/item/TVP_1973_18_2_a13/
@article{TVP_1973_18_2_a13,
author = {P. Kouznetzoff and A. S. Yudina},
title = {Some {Asymptotic} {Expansions} for an {Incomplete} {Probability} {Integral}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {367--371},
year = {1973},
volume = {18},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_2_a13/}
}
TY - JOUR
AU - P. Kouznetzoff
AU - A. S. Yudina
TI - Some Asymptotic Expansions for an Incomplete Probability Integral
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1973
SP - 367
EP - 371
VL - 18
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1973_18_2_a13/
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%A A. S. Yudina
%T Some Asymptotic Expansions for an Incomplete Probability Integral
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1973
%P 367-371
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%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1973_18_2_a13/
%G ru
%F TVP_1973_18_2_a13
For the D. Owen function $$ T(h,a)=\frac{1}{2\pi}\int_0^a e^{-\frac{h^2}{2}(1+x^2)}\frac{dx}{1+x^2} $$ asymptotic expansions are derived in the cases 1) $h\to\infty$, $a\to 1$, 2) $h\to\infty$, $a\to 0$. Numerical computations by the formulas obtained are given. A correspondence between $T(h,a)$ and an incomplete probability integral is established.
