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Results tagged with sequences-and-series
Search options questions only
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user 9550
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
3
votes
1
answer
241
views
Reconstructing analytic tetration with a complex height from a thinner set of points
This is a follow-up to my previous question An explicit series representation for the analytic tetration with complex height.
Recall the definition $(11)$ from there:
$$t(z) = \sum_{n=0}^\infty \sum_ …
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42
votes
2
answers
2k
views
Numbers that are generic w.r.t. exponentiation
This is a follow-up to my old question Number of distinct values taken by $x\hat{\phantom{\hat{}}}x\hat{\phantom{\hat{}}}\dots\hat{\phantom{\hat{}}}x$ with parentheses inserted in all possible ways.
…
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29
votes
3
answers
3k
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An explicit series representation for the analytic tetration with complex height
Tetration is the next hyperoperation after more familiar addition, multiplication and exponentiation. It can be seen as a repeated exponentiation, similar to how exponentiation can be seen as a repeat …
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18
votes
3
answers
1k
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A curious series related to the asymptotic behavior of the tetration
The tetration is denoted $^n a$, where $a$ is called the base and $n$ is called the height, and is defined for $n\in\mathbb N\cup\{-1,\,0\}$ by the recurrence
$$
{^{-1} a} = 0, \quad {^{n+1} a} = a^{\ …
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10
votes
1
answer
750
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A conjecture about certain values of the Fabius function
The Fabius function is a smooth monotone function $F:[0,1]\to[0,1]$, satisfying functional equations
$$F(0)=0, \quad F(1-x)=1-F(x)\tag1$$
and
$$F'(x) = 2 \,F(2 x) \quad \text{for} \,\, 0<x<1/2.\tag2$$ …
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