For-some-constant-0-1-calculate-0-e-t-xt-dt-2pi-1-x-2-1-1-e-1-x-1-x-0-

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

For some constant α \in (0, 1)

calculate : \int_{0}^{\infty} e^{- \frac{t^{α}}{α} - xt} dt \sim \sqrt{\frac{2 π}{1 - α}} \cdot x^{- \frac{α}{2 (1 - α)} - 1} e^{\frac{1 - α}{α} \cdot x^{- \frac{α}{1 - α}}}, x \to 0^{+}