I've been working on this integral for ages and I can't seem to figure it out. I can coax Mathematica to solve it for special values of $\alpha$ (integers and tidy fractions), and those special cases tend to include lots of generalized hypergeometric functions, which makes me think the general form must be pretty wild. I've pored over Gradshteyn & Ryzhik, trying to do pattern matching on this integral and various substitutions of it, with no luck. Any ideas?
2026-04-10 21:37:53.1775857073
Evaluate $\int_0^\infty e^{-(x^2+1)^\alpha}$, when $0 < \alpha < 2$
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