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Aug 2, 2022 at 15:21 vote accept Iosif Pinelis
Apr 29, 2022 at 19:29 comment added Iosif Pinelis @T.Amdeberhan : Thank you for your further comment. Taking the log indeed helps.
Apr 29, 2022 at 19:16 history edited Iosif Pinelis CC BY-SA 4.0
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Apr 29, 2022 at 19:16 answer added Iosif Pinelis timeline score: 2
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Apr 29, 2022 at 18:59 history edited Iosif Pinelis CC BY-SA 4.0
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Apr 29, 2022 at 18:42 comment added T. Amdeberhan Also, what you put in the questions, such as #1, and restricting to $f_1(t)$, a similar manifestation works for the series of $F_1(t)=\frac{1-t}2\log\left(\frac{1+t}{1-t}\right)$. Inherited by $f_1(t)$. But, it is easier to see in $F_1(t)$ than $f_1(t)$.
Apr 29, 2022 at 18:37 comment added Iosif Pinelis @T.Amdeberhan : Yes, of course. Thank you for your comment. It may be interesting that apparently $f_1^{(2k)}(0)/(2k)!=f_1^{(2k+1)}(0)/(2k+1)!$ for all $k=0,1,\dots$.
Apr 29, 2022 at 18:28 comment added T. Amdeberhan In analyzing $f(t)$, it might suffice to study one part of $f$. That is, $f_1(t)=\left(\frac{1+t}{1-t}\right)^{(1-t)/2}$. I'm sure you knew that.
Apr 29, 2022 at 16:18 history asked Iosif Pinelis CC BY-SA 4.0