User Gottfried Helms

19 votes

Is there always one integer between these two rational numbers?

answered Sep 3, 2017 at 21:07

18 votes

Accepted

Eigenvalues of infinite matrices

answered Oct 15, 2012 at 0:48

13 votes

Structures in the plot of the “squareness” of numbers

answered Nov 21, 2016 at 17:29

12 votes

Larger cycle than 4, 2, 1 in Collatz iteration?

answered Jun 24, 2011 at 19:33

11 votes

Is $ \sum\limits_{n=0}^\infty x^n / \sqrt{n!} $ positive?

answered Jan 5, 2012 at 22:29

11 votes

German mathematical terms like "Nullstellensatz"

answered Apr 19, 2011 at 9:05

10 votes

The functional equation $f(f(x))=x+f(x)^2$

answered Dec 18, 2010 at 11:07

9 votes

Do complex iterates of functions have any meaning?

answered Jul 27, 2011 at 22:37

9 votes

3n+1 problem and cycles

answered Mar 16, 2015 at 11:36

9 votes

A curious series related to the asymptotic behavior of the tetration

answered Jun 14, 2017 at 8:09

7 votes

Unexpected behavior involving √2 and parity

answered Feb 28, 2020 at 16:20

7 votes

Accepted

How to prove that this equation has only one solution?

answered Jun 25, 2015 at 12:08

7 votes

A question on Collatz's conjecture:proportion of "low flying" orbits

answered Feb 21, 2015 at 14:25

7 votes

On an example of an eventually oscillating function

answered Mar 2, 2015 at 18:16

7 votes

Is there an "elegant" non-recursive formula for these coefficients? Also, how can one get proofs of these patterns?

answered Mar 8, 2011 at 18:59

6 votes

Longest coinciding pair of integer sequences known

answered Jan 15, 2011 at 5:03

6 votes

Accepted

Inequality of arithmetic, geometric and harmonic means

answered Sep 11, 2014 at 3:26

5 votes

Does the formal power series solution to $f(f(x))= \sin( x) $ converge?

answered Mar 11, 2016 at 22:33

5 votes

Eigencircles of n x n matrices?

answered Apr 27, 2012 at 3:45

5 votes

Implication for cycles (of some length $m$) in Collatz-type problems: typical ratio between largest and smallest element?

answered Oct 15, 2011 at 19:01

5 votes

The functional equation $f(f(x))=x+f(x)^2$

answered Dec 19, 2010 at 17:06

5 votes

The factorials of -1, -2, -3, …

answered Jul 17, 2010 at 18:39

5 votes

$f(f(x))=\exp(x)-1$ and other functions "just in the middle" between linear and exponential

answered Nov 3, 2010 at 11:07

5 votes

Inverse of the Riemann zeta function

answered Aug 10, 2011 at 11:53

5 votes

Abel summation of the alternating series of primes?

answered May 28, 2011 at 13:24

5 votes

Is $ \sum\limits_{n=0}^\infty x^n / \sqrt{n!} $ positive?

answered Jan 6, 2012 at 5:15

5 votes

Irrationality of generalized continued fractions

answered Mar 2, 2017 at 1:22

4 votes

Conjecture about harmonic numbers

answered Jan 27, 2017 at 10:17

4 votes

How to solve $f(f(x)) = \cos(x)$?

answered Mar 15, 2017 at 13:32

4 votes

Does 53 diverge to infinity in this Collatz-like sequence?

answered Mar 16, 2017 at 2:16

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112 Answers

Is there always one integer between these two rational numbers?

Eigenvalues of infinite matrices

Structures in the plot of the “squareness” of numbers

Larger cycle than 4, 2, 1 in Collatz iteration?

Is $ \sum\limits_{n=0}^\infty x^n / \sqrt{n!} $ positive?

German mathematical terms like "Nullstellensatz"

The functional equation $f(f(x))=x+f(x)^2$

Do complex iterates of functions have any meaning?

3n+1 problem and cycles

A curious series related to the asymptotic behavior of the tetration

Unexpected behavior involving √2 and parity

How to prove that this equation has only one solution?

A question on Collatz's conjecture:proportion of "low flying" orbits

On an example of an eventually oscillating function

Is there an "elegant" non-recursive formula for these coefficients? Also, how can one get proofs of these patterns?

Longest coinciding pair of integer sequences known

Inequality of arithmetic, geometric and harmonic means

Does the formal power series solution to $f(f(x))= \sin( x) $ converge?

Eigencircles of n x n matrices?

Implication for cycles (of some length $m$) in Collatz-type problems: typical ratio between largest and smallest element?

The functional equation $f(f(x))=x+f(x)^2$

The factorials of -1, -2, -3, …

$f(f(x))=\exp(x)-1$ and other functions "just in the middle" between linear and exponential

Inverse of the Riemann zeta function

Abel summation of the alternating series of primes?

Is $ \sum\limits_{n=0}^\infty x^n / \sqrt{n!} $ positive?

Irrationality of generalized continued fractions

Conjecture about harmonic numbers

How to solve $f(f(x)) = \cos(x)$?

Does 53 diverge to infinity in this Collatz-like sequence?