Geodesic
Some Asymptotic Expansions for an Incomplete Probability Integral
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 2, pp. 367-371

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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. 
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     title = {Some {Asymptotic} {Expansions} for an {Incomplete} {Probability} {Integral}},
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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/