Why Owen's selected this function $f(h,x)=\frac{e^{-\frac 12 h^2(1+x²)}}{1+x²}$ for integration?

Question

Owen's function defined as $T$ Owen's function such that :$$T(h,a)=\displaystyle\int_{0}^{a}\frac{e^{-\frac 12 h^2(1+x^2)}}{1+x^2}\,\mathrm dx$$ ,My question here is not about this integral but why Owen's selected or choosed this function : $\displaystyle f(h,x)=\frac{e^{-\frac 12 h^2(1+x^2)}}{1+x^2}$ for integration ? or just it is of the Gaussian form ? Are there any interesting mathematical properties about it ? Is there any reference discussed the history of this function ?