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Results tagged with sequences-and-series
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user 4507
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
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Is there any numerical technique to sum x^(n^alpha), n=0,1,...?
I've come across this infinite series: $\sum_{n=0}^\infty x^{n^\alpha}$, with $0<x<1$ and $\alpha > 0$.
Does this series have a name and/or is there a method for computing it (besides brute force, o …
- 143
2
votes
1
answer
270
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Can we find an l-2 sequence if we know all l-p norms?
I'm wondering if there is a way to approximate the first $M$ terms of a non-increasing $\ell^2$ sequence $\{c_n\}$ if we know
$|c|_p^p = \sum c_n^p$ for $p=2,3,4,\dots$?
I've tried truncating the …
- 143
1
vote
Can we find an l-2 sequence if we know all l-p norms?
Sorry to answer my own question, but having thought about it more, I realize this is impossible unless you have arbitrarily high precision for all the $|c|_p$'s. The reason is, as $p$ grows, the lead …
- 143