The infinite-sequences tag has no usage guidance.

**2**

votes

**1**answer

86 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

**1**answer

108 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

**1**answer

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

**1**answer

126 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

**1**answer

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

**1**answer

173 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

**0**answers

243 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

**2**answers

196 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

**1**answer

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

**2**answers

324 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

**2**answers

372 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

**2**answers

483 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

**0**answers

467 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

**1**answer

839 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

**2**answers

465 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

**1**answer

497 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 ...

**0**

votes

**4**answers

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 ...