Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with sequences-and-series
Search options questions only
not deleted
user 3106
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.
9
votes
2
answers
2k
views
Why does this theta function value yield such a good Riemann sum approximation?
Let $T(q)$ denote the third Jacobi theta function at $z=0$; i.e.,
$$T(q) := \sum_{n\in\mathbb{Z}} q^{n^2}.$$
Then for any $x>0$, $T(\exp(-1/x)) \approx \sqrt{\pi x}$. For example, as the entry for A19 …
- 149k
71
votes
8
answers
12k
views
Possible new series for $\pi$
In a recent (unfortunately over-hyped) preprint by Saha and Sinha, Field theory expansions of string theory amplitudes (arXiv:2401.05733), they present the following series for $\pi$:
$$\pi = 4 + \sum …
- 2,836
86
votes
4
answers
11k
views
Nonexistence of boundary between convergent and divergent series?
The following is a FAQ that I sometimes get asked, and it occurred to me that I do not have an answer that I am completely satisfied with. In Rudin's Principles of Mathematical Analysis, following Th …
- 1,446
13
votes
5
answers
1k
views
Asymptotics of a Bernoulli-number-like function
Tony Lezard asked me the following question which seemed like it should not be too hard but which I did not immediately see how to answer. Define $f(n,k)$ recursively by $f(1,k) = 1$ and
$$f(n,k) = \ …
- 82.7k