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Dark Malthorp
  • Member for 4 years, 4 months
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17 votes
0 answers
255 views

If $r\in\mathbb{Q}\setminus\mathbb{Z}$ is it possible that $r^{r^{r^r}}\in \mathbb{Q}$?

10 votes
0 answers
217 views

Find radius of convergence for a complicated series for $f'(f(x)) = f(f'(x))$

9 votes
1 answer
215 views

Given $f(z)$ can you find $g(z)$ such that $g(z+1) = f(z) + g(z)$

8 votes
1 answer
215 views

$f(z) = z + f(z^2)$ outside the unit disk?

7 votes
1 answer
176 views

Evaluate $\lim\limits_{n\rightarrow\infty} \mathrm{srt}_n\left({^{n+1}}2\right)$

6 votes
1 answer
281 views

Constructing analytic solutions to the delay differential equation $f'(x) = x f(x-1) - f(x)$

5 votes
0 answers
190 views

Real, analytic exponential factorial $f(x) = x^{f(x-1)}$

5 votes
2 answers
270 views

Does anyone know a simple proof of $\lim_{x\rightarrow\infty} x\int_0^1 t^{x t} dt = 1$

4 votes
1 answer
111 views

Does this identity with binomial coefficients have a combinatorial interpretation? [duplicate]

4 votes
2 answers
202 views

How to find the divergence rate of a recursive sequence defined by $s_n = s_{n-1}(1 + c_n s_{n-1})$

2 votes
1 answer
44 views

Taylor series boundary behavior if the coefficients are not absolutely summable

2 votes
0 answers
77 views

Is anything known about functions of the type $f(z) = \sum_{n=0}^\infty z^{a_n}$, where $a_n$ is an integer sequence?

2 votes
1 answer
122 views

How bad can a Taylor series be?

2 votes
0 answers
65 views

How to show convergence of the series sum over zeroes of the zeta function

2 votes
0 answers
51 views

Is there a function whose Dirichlet series and whose Taylor series are the same?

2 votes
1 answer
69 views

Can every computable number be written as a limit of a termwise-definable sequence?

1 vote
0 answers
26 views

If there a way to simplify the condition that $\mathbb{E}\left(\inf\{n : X_n > n\}\right) < \infty$, where $X_n$ is i.i.d.?

1 vote
1 answer
38 views

Is there any bound to how quickly or slowly an enumeration of the rationals diverges?

1 vote
0 answers
23 views

How to characterize the random variables $X$ with values on $[0,1]$ such that $X \stackrel{d}{=} |2X-1|$?

1 vote
0 answers
25 views

Can $\sum_{n=1}^\infty \frac{x - a_n}{(x-a_n)^2 + b_n^2}$ be positive for all $x$ in $\mathbb{R}$?

1 vote
0 answers
39 views

Can an algebraic function be written as a composition of polynomials and their inverses?

0 votes
0 answers
82 views

How to invert this type of infinite series?

0 votes
0 answers
54 views

Are there any methods for finding analytic solutions to this equation $(xy + \frac1e)e^{F(x,y)} = F(g(y)x , f(y))$

0 votes
0 answers
216 views

Differential equation with infinite initial value

0 votes
0 answers
109 views

Why are these two functions different for negative numbers?

0 votes
0 answers
81 views

What is the limiting behavior of a Taylor series?

0 votes
0 answers
39 views

Given an analytic function with $f(0) = 0$, $\Vert f'(0)\Vert= 1$, when I can I find an open invariant set?