For a given $\alpha \in (0,2)$ How fast does
\begin{equation} \int_{\pi/h}^\infty{\exp(-p^\alpha)}\,\mathrm{d}p \end{equation}
go to zero as $h$ goes to zero? Any upper bound on the speed of convergence would be great!
For a given $\alpha \in (0,2)$ How fast does
\begin{equation} \int_{\pi/h}^\infty{\exp(-p^\alpha)}\,\mathrm{d}p \end{equation}
go to zero as $h$ goes to zero? Any upper bound on the speed of convergence would be great!
Hint: use integration by parts
Hint2: to simplify the calculation. Substitute first $x=p^\alpha$
Hint3: you should get the result $\sim (\pi/h)^{1-\alpha} e^{-(\pi/h)^\alpha} \alpha^{-1}$