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Dec 18, 2021 at 15:26 comment added Richard Stanley Note that if $x$ is a nonnegative integer, then $f_1(x)=f(x)$.
Dec 18, 2021 at 14:16 history edited Martin Sleziak
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Nov 22, 2019 at 14:28 history edited Max Alekseyev
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Nov 22, 2019 at 3:23 answer added Max Alekseyev timeline score: 1
Feb 14, 2014 at 8:19 review Close votes
Feb 14, 2014 at 10:18
Feb 12, 2014 at 9:44 comment added Greg Martin Presumably each of these formulas came from somewhere - some method of representing $f(x)$? If so, why don't those sources already prove that the expressions are equal where defined?
Feb 12, 2014 at 9:15 comment added Daniel Litt I don't see why this is being downvoted. This doesn't seem trivial and the motivation Anixx gives in the comment is absolutely fine.
Feb 12, 2014 at 8:41 comment added Anixx @UwF the motivation is as follows: the first one is the Newton series, but it is not applicable to the cases where the function has poles. The third one can be easily generalized to the cases where the function has poles in integer points and also it can be made symmetric around zero. So the third one is more general, while the first one is easier to analyze convergence. The third one also converges much faster. My interest about the second one is purely curiosity.
Feb 12, 2014 at 8:15 history asked Anixx CC BY-SA 3.0