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Sep 8 at 17:15 vote accept yfful
Sep 4 at 19:18 answer added Iosif Pinelis timeline score: 2
Sep 4 at 13:50 comment added yfful Thanks @IosifPinelis for the comment. I think we need more conditions on $\alpha$, $\beta$ and $\lambda$. I have editted the question for the regimes of my interest.
Sep 4 at 13:50 history edited yfful CC BY-SA 4.0
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Sep 4 at 13:13 comment added Iosif Pinelis If $\lambda$ is small, then $M:=\max f>2$, and then the integral will behave somewhat like $(1-M)^n$ for large $n$. So, the behavior of the integral will depend very much on $\alpha,\beta,\lambda$.
Sep 4 at 13:01 history edited yfful CC BY-SA 4.0
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Sep 4 at 12:19 comment added gmvh Welcome to MO! May I ask where this integral comes from?
S Sep 4 at 12:13 review First questions
Sep 4 at 12:19
S Sep 4 at 12:13 history asked yfful CC BY-SA 4.0