Questions tagged [gm.general-mathematics]
Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
362 questions
6
votes
4
answers
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Writing an equation with cases when case description is long
This question seeks advice on what is common or at least acceptable in typing a certain inequality in a research paper.
I have an inequality that looks like this:
\begin{equation*}
f_{a,b,c}(x)\leq
\...
- 868
20
votes
14
answers
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views
Great theorems with elementary statements: 2026-onward [closed]
My 2021 book
Landscape of 21st Century Mathematics, Selected Advances, 2001–2020
collects great theorems with elementary statements published in 2001-2020. I now finishing the second edition of this ...
3
votes
4
answers
492
views
Closed form for a hypergeometric sum
Sorry if this is too simple but, I came across the following sum
$$\sum_{k=0}^n (-1)^{n-k} \frac{(2(n-k)-1)!!}{(2k)!!}x^{2k}$$
where $n!!$ is the double factorial.
I am asking if it has some closed ...
0
votes
0
answers
61
views
Can this nested sum with delta constraint be simplified to a compact form?
I would like to simplify the following nested sum expression, defined for integers $n, k \ge 0$:
$$
\sum_{i_n=0}^k (n - k + i_n)
\sum_{i_{n-1}=0}^{k - i_n} (n{-}1 - (k{-}i_n) + i_{n-1}) \cdots
\sum_{...
- 11
1
vote
1
answer
306
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About recurrent sums
Recently I'm doing a research and I'm facing a lot of "recurrent" sums, I found one nice arxiv paper about them, the definition of a recurrent sum is as follows:
A recurrent sum is any sum ...
2
votes
2
answers
284
views
Particular inversion of a multiple sum
I am dealing with a problem involving the inversion of multiple sums:
While analyzing a recurrence relation, I reached a stage where I need to invert a nested sum of the form:
$$
\sum_{k=0}^{\lambda n}...
-1
votes
1
answer
185
views
Inversion of a particular multiple sum
To those who are familiar with inversion of multiple sums, I'm stuck with the following problem:
How to invert the following multiple sum ?
$$\sum_{k=0}^{N}\sum_{i_n=0}^{N-k}\left(\sum_{i_{n-1}=0}^{...
50
votes
2
answers
4k
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How do mathematical developments make their way into the mass media?
This question may seem off topic, and feel free to express that, but first let me say why I think it belongs here.
Every so often there are articles in mainstream newspapers, and also in popular ...
6
votes
1
answer
604
views
Format of solution to AMM problem
This is a rather 'soft' question, but I have solved an AMM problem and want to submit a solution. However I couldn't find on the website what format they want it in? They have advice for papers/notes ...
user550547
5
votes
0
answers
338
views
I want to study math. & I.am 50 years. Is it possible? [closed]
I did my graduation but I want to study higher math as a passion. My age is 50. Is it possible ?
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votes
14
answers
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When is 4 qualitatively different than $n\leq 3$?
Inspired by When is 2 qualitatively different from 3?
Also similar to Are there mathematical concepts that exist in dimension 4, but not in dimension 3? (Math SE), but with the restriction of being ...
61
votes
77
answers
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When is 2 qualitatively different from 3?
I'd like to get a list of instances in mathematics where a problem with two parameters (or some parameter set to $2$) is qualitatively different from the instance of that problem with the value set to ...
1
vote
3
answers
491
views
What is the mixed-radix numeral system of best radix economy?
Radix economy concerns itself with the efficiency of encoding numbers. For positional number systems that use a fixed base, base three is the most efficient choice among the integers, and $e$ is the ...
- 111
15
votes
6
answers
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What does keep you "doing what you do"? [closed]
I am towards the end of my Phd (with some difficultues to overcome, I can say I am really satisfied about it) and I was wondering about what to do next. There are basically two paths: academia or ...
- 835
2
votes
1
answer
606
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What are some (popular) references on variants of the classical gambler's ruin problem that exists in literature?
It is fascinating that the gambler's ruin problem which is so ubiquitous in modern probability theory (cf. the Levin-Peres text on Markov chain and Mixing Times) actually dates back to a letter from ...
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