How would you evaluate this integral? \begin{equation}\int_{0}^{\infty}\frac{dx}{\sqrt{x}}\, e^{-x^{2}-\frac{b^{2}}{x}}\end{equation} It reminds me of the form of a modified Bessel function of the second kind, but is slightly different because of the $x^{2}$ term. I can series expand it in terms of a sum of Gamma functions, but I don't know what that sum converges to.
2026-05-15 16:30:04.1778862604
Closed form for this integral $\int_{0}^{\infty}\frac{dx}{\sqrt{x}}\, e^{-x^{2}-\frac{b^{2}}{x}}$
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