$\sum_{n=0}^{k}f(n)$ is the notation for $f(0)+f(1)+f(2)+...f(k)$
$\prod_{n=0}^{k}f(n)$ is the notation for $f(0)\cdot f(1)\cdot f(2)\cdot ...f(k)$.
What would the notation be to describe this $f(k)^{f(k-1)^{f(k-2)...^{f(0)}}}$ be?
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2$\begingroup$ You may want to look into tetration. The point is, even the case where the $f(i)$'s are constant is somewhat niche and obscure, so I doubt there is a consistent notation across the literature for this concept. $\endgroup$– silvascientistCommented Nov 18, 2017 at 2:38
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$\begingroup$ @MonstrousMoonshiner so I could just honestly make one up? I need it for a project $\endgroup$– user406613Commented Nov 18, 2017 at 2:39
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1$\begingroup$ How about $$\uparrow_{n=0}^kf(n)$$ $\endgroup$– Gerry MyersonCommented Nov 18, 2017 at 2:50
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$\begingroup$ @GerryMyerson I'll call it myerson notation, I was just gonna use an uppercase e ���😂😂 $\endgroup$– user406613Commented Nov 18, 2017 at 2:50
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$\begingroup$ @script8man That might be a little hasty, I would suggest asking your teacher or advisor about it before you go ahead and do something like that. $\endgroup$– silvascientistCommented Nov 18, 2017 at 2:55
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