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-4
votes
0answers
13 views

Good estimates on the truncation of the exponential series. [closed]

What are the good (analytic) upper bounds we have on the series $\sum_{k=D}^\infty \frac{a^k}{k!}$ in terms of $a$ and $D$?
4
votes
2answers
223 views

Moment problem on [-1,1]: necessary and sufficient conditions

Consider a sequence of real numbers $s=(s_0,s_1,\ldots)$. When is there a Borel measure $\mu$ supported on $[-1,1]$ so that $$ s_k = \int_{[-1,1]} x^k\,\mathrm{d}\mu,\quad \forall k\in\mathbb N\;? $$ ...
2
votes
2answers
82 views

Sum of subsequence, over index set of non-zero density, of monotone divergent sum also divergent?

For a subset $S$ of the natural numbers $N$ and $n\in N$ let $|S\cap n|$ be the number of members of $S$ that are less than $n$. Suppose $S$ does not have upper asymptotic density $0$. That is, ...
2
votes
2answers
303 views

Non-Formal Applications: Higman and Kruskal

After looking through many papers, I noticed that most of the discussions and proofs for Higman's Lemma and Kruskal's Tree Theorem only have formal applications in set theory, logic, and type theory. ...
3
votes
1answer
154 views

Hermite-Kakeya Theorem for entire functions

In a question asked by Bobby Ocean, the following theorem is cited: Hermite-Kakeya Theorem(for polynomials) - Given two real-valued polynomials, $f$ and $g$, then $f(x)+g(x) r$ has only real zeros ...
2
votes
1answer
101 views

Asymptotic expansion of a sequence given by an integral with reciprocal Gamma function

I would like to know the asymptotic expansion of the sequence of positive numbers given by $$I_{n}:=-\int_{0}^{1}\frac{n^{x-1}}{\Gamma(x-1)}dx,$$ for $n\rightarrow\infty$. One can easily derive an ...
-2
votes
1answer
114 views

Looking for the name of an infinite sequence [closed]

I am looking for information about a sequence that seems like it should converge. The sequence is textually described as: ...
3
votes
1answer
49 views

Complete classification of complexity classes / infinite approaching sequences

http://en.wikipedia.org/wiki/Time_complexity#Table_of_common_time_complexities For complexity as seen in the above link, complexity classes can be log, polynomial, exp, or composition of any of these ...
2
votes
1answer
132 views

Is there a dense rational sequence of positive separation?

Let us consider the set $\ell_\neq$ of bounded sequences of unequal real terms. We use the following descriptions. A sequence $x=(x_0,x_1,...)\in\ell_\neq$ is dense if, for all $\varepsilon>0$, ...
0
votes
1answer
169 views

Lemma about infinite sequences we are hoping is true [closed]

Given N infinite sequences of non-negative integers, some of which diverge to infinity, must there exist two steps i, j in which $x_i \leq x_j$ for all sequences x?
2
votes
1answer
202 views

Iterated projections in Hilbert spaces

Let $E$ be an Hilbert space and $F, G$ two subspaces such that $F \cap G =\{0\}$. Let $(x_n)$ be the sequence of iterated orthogonal projections: $x_0 \in F$, $x_1$ is the orthogonal projection of ...
0
votes
0answers
292 views

Greedy sequences without k-term arithmetic progressions

If $S_k$ is the greedy sequence with no length-k arithmetic subsequence, (ie $S_3$ = A003278 , $S_4$ = A005837 , $S_5$ = A020655 ), is it guaranteed that any other sequence $a$ with no length-k ...
0
votes
2answers
203 views

sequence, such that sum of any combinations in the sequence does not equal another [closed]

Hi, Is there any known sequence such that the sum of a combination of one subsequence never equals another subsequence sum. The subsequences should have elements only from the parent sequence. ...
-2
votes
1answer
202 views

How to work with infinite random graph(s) ?

Hi, In the case where we are dealing with an infinite random graph (RG with infinite nodes). How do we model/work with notions like degrees, degree distribution ? How are they defined ? Thanks!
1
vote
2answers
328 views

sum of infinite series

Given the complex variable $x$, complex constant $c$, and integer number $r$. I want to solve the equation: $\sum_{k=1}^{\infty}\frac{e^{kx}}{k^r}=c$. I was thinking that if there is a formula or ...
2
votes
2answers
404 views

Is it necessary that gcd > 1 of an infinite set? [closed]

Consider an infinite set $S$, of positive integers. If all the finite subsets of $S$ have GCD $>$ $1$, is it necessary that the GCD of $S$ is greater than $1$ as well?
2
votes
2answers
523 views

References for the result that $\sqrt{n}$ is equidistributed mod 1

It is not difficult to show (even without Weyl criterion) that the sequence $\sqrt{n}$, $n=1,2,\ldots$ is equidistributed mod 1. However, I need a reference to this result. Can you help me? Thanks.
0
votes
0answers
589 views

In a network with N nodes, what is the general formula for computing the propagation of a set of numbers?

I am creating a circular neural network with N nodes. Each node is connected via a send pathway to every other node, and the connection between two nodes has a weight. Any number sent over the ...
13
votes
1answer
854 views

Self-avoiding walk on $\mathbb{Z}$

This one is an unanswered question in Math.SE. I've posted it here because I think it deserves more attention. How many sequences $\{a_n\}$ exist satisfying: a) $a_1=0$ b) $\forall k\ge1 $ ...
4
votes
2answers
533 views

Ends of topological spaces. Why independent of choice of ascending sequence of compact subsets?

Quoting from http://en.wikipedia.org/wiki/End_(topology): "Let X be a topological space, and suppose that K1 ⊂ K2 ⊂ K3 ⊂ · · · is an ascending sequence of compact ...
7
votes
1answer
509 views

Magic square on an infinite lattice

This question came to me while reading the discussion of magic square in the complex plane with equal integrals along every horizontal, vertical and diagonal "magic square in the complex plane with ...
1
vote
4answers
3k views

Does Cauchy continuity imply uniform continuity? [No.] [closed]

It is well known that if $X$ is a first countable topological space and $Y$ is a topological space, then $f : X \rightarrow Y$ is continuous iff $$\forall x \in {\rm map}(\mathbb{N},X),\forall p \in X ...