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Question Number 166735 by qaz last updated on 26/Feb/22

$$\mathrm{For}\mathrm{some}\mathrm{constant}\alpha \in (0,1)$$$$\mathrm{calculate}:{\int }_0^{\mathrm{\infty }}{\mathrm{e}}^{-\frac{{\mathrm{t}}^{\alpha }}{\alpha }-\mathrm{xt}}\mathrm{dt}\sim \sqrt{\frac{2\pi }{1-\alpha }}\cdot {\mathrm{x}}^{-\frac{\alpha }{2(1-\alpha )}-1}{\mathrm{e}}^{\frac{1-\alpha }{\alpha }\cdot {\mathrm{x}}^{-\frac{\alpha }{1-\alpha }}},\mathrm{x}\to 0^{+}$$

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