User Gottfried Helms

13 votes

1 answer

782 views

Cesaro(?)/Euler(?) - summation of the $s(p)=\sum_{k=0}^\infty (-1)^{H(k)} (1+k)^p$ for $p=1,2,3,...$ (where $H(k)$ is the Hamming-weight)

asked May 23, 2014 at 6:28

9 votes

1 answer

824 views

An infinite set of identities using Stirling numbers 1st kind - are they all zero?

asked Aug 9, 2012 at 17:12

9 votes

1 answer

598 views

Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity

asked Dec 14, 2013 at 14:24

8 votes

2 answers

296 views

How to formalize the loci of equal arg($\zeta(s)$) ("isogones") in the near of a nontrivial root

asked Oct 18, 2015 at 10:11

7 votes

2 answers

570 views

For an approach to the Hadamard-matrix-problem: is there a proof, that the iterative plane-wise orthogonal rotations (Quartimax/Varimax) converge to global maximum?

asked Mar 8, 2012 at 9:09

7 votes

1 answer

652 views

Fermat-quotient of "order" 3: I found $68^{112} \equiv 1 \pmod {113^3}$ - are there bigger examples known?

asked Dec 6, 2013 at 16:15

6 votes

0 answers

197 views

"Bell" or "Jabotinsky"-matrix - What's the canonical name (if any)?

asked Oct 15, 2012 at 10:12

6 votes

1 answer

454 views

Efficient (divergent) summation for sum of zetas at negative arguments?

asked Apr 18, 2013 at 14:21

6 votes

0 answers

733 views

$f(x) \ne g(x)$ but $f(f(x))=g(g(x))$ - is there a name/some discussion of this property?

asked Aug 27, 2011 at 5:35

6 votes

4 answers

487 views

When is $\{b^2 - \{b-1\}_2\}_2=1$ with odd $b$? (The bracket-notation explained below)

asked Oct 19, 2020 at 11:10

5 votes

1 answer

571 views

Can I assign the term "is eigenvector" and "is eigenmatrix" of matrix $P$ in my specific (infinite-size) case?

asked Dec 6, 2019 at 12:04

5 votes

1 answer

742 views

mertens-function in the light of divergent summation - what summation method were best adapted

asked Nov 26, 2010 at 23:15

5 votes

0 answers

223 views

Oscillation aspects of two-way infinite alternating series (a followup from the MO-question "functions that eventually oscillate")

asked Mar 26, 2015 at 3:54

4 votes

1 answer

448 views

Is that series-transformation known in the context of divergent summation?

asked Mar 10, 2011 at 15:59

4 votes

1 answer

404 views

Can the relative count of the primefactors in $\small \lim_{w\to\infty}\prod_{k=1}^w (p_k-1) $ be determined analytically?

asked Dec 19, 2011 at 22:13

4 votes

2 answers

503 views

How to check numerical precision of my computation of Stieltjes-constants?

asked Aug 26, 2012 at 14:31

3 votes

0 answers

270 views

Alternating sums of powers of the lngamma ($\small f_p(x) = \sum \log(k!)^p x^k $ at $\small x=-1$)

asked Jan 31, 2012 at 7:23

3 votes

1 answer

357 views

Is there a systematic relation between the generating functions for the rows vs that for columns of infinite sized Carleman-matrices?

asked Jun 9, 2015 at 20:29

3 votes

0 answers

256 views

What would be a better method for numerical diagonalization of a certain Vandermonde-like matrix?

asked Oct 17, 2013 at 9:17

3 votes

1 answer

578 views

What is the (fractional) half-derivative of zeta at $s=0$ (and how to compute it)?

asked May 4, 2013 at 7:49

3 votes

0 answers

237 views

Who defined the term "Carleman-matrix" and also their properties as they are?

asked Jun 27, 2017 at 13:05

2 votes

0 answers

350 views

Fractional iteration of a variant of the $\sin()$ function - how to fractionally iterate $ f(x)=\sum_{k=1}^\infty (-1)^k a_{2k}x^{2k}$?

asked Jul 4, 2017 at 22:37

2 votes

0 answers

68 views

Question about a set of Laplace-transforms

asked Mar 19, 2018 at 22:57

1 vote

0 answers

271 views

Is my ansatz for finding $n$-periodic-points of the exponential-function exhaustive?

asked May 23, 2020 at 8:25

1 vote

1 answer

502 views

A Zsigmondy-theorem-analogy in the generalized Collatz-problem $3x+\rho$?

asked Sep 4, 2017 at 7:33

1 vote

0 answers

145 views

Any possible way to invert a function built from a sum of two?

asked Jun 11, 2013 at 10:56

1 vote

1 answer

663 views

What are conditions to make f(x) defined by f(x)=f(x-1)*x + 1/e unique(for instance convex)?

asked Nov 8, 2010 at 22:28

0 votes

1 answer

259 views

Efficient way for computation of derivatives of $f(x) = \zeta(1-x) + 1/x $ at integer x?

asked Mar 8, 2013 at 17:18

0 votes

0 answers

168 views

Is there an option to handle Neumann-series when it diverges? (using infinite-sized Carleman matrices)

asked Oct 18, 2018 at 13:36

0 votes

1 answer

366 views

On the relevance of the property $\exp^{\circ a}(\exp^{\circ b}(z))=\exp^{\circ a+b}(z)$ for the fractional iteration ("tetration")

asked May 3, 2021 at 8:31

Stack Exchange Network

30 Questions

Cesaro(?)/Euler(?) - summation of the $s(p)=\sum_{k=0}^\infty (-1)^{H(k)} (1+k)^p$ for $p=1,2,3,...$ (where $H(k)$ is the Hamming-weight)

An infinite set of identities using Stirling numbers 1st kind - are they all zero?

Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity

How to formalize the loci of equal arg($\zeta(s)$) ("isogones") in the near of a nontrivial root

For an approach to the Hadamard-matrix-problem: is there a proof, that the iterative plane-wise orthogonal rotations (Quartimax/Varimax) converge to global maximum?

Fermat-quotient of "order" 3: I found $68^{112} \equiv 1 \pmod {113^3}$ - are there bigger examples known?

"Bell" or "Jabotinsky"-matrix - What's the canonical name (if any)?

Efficient (divergent) summation for sum of zetas at negative arguments?

$f(x) \ne g(x)$ but $f(f(x))=g(g(x))$ - is there a name/some discussion of this property?

When is $\{b^2 - \{b-1\}_2\}_2=1$ with odd $b$? (The bracket-notation explained below)

Can I assign the term "is eigenvector" and "is eigenmatrix" of matrix $P$ in my specific (infinite-size) case?

mertens-function in the light of divergent summation - what summation method were best adapted

Oscillation aspects of two-way infinite alternating series (a followup from the MO-question "functions that eventually oscillate")

Is that series-transformation known in the context of divergent summation?

Can the relative count of the primefactors in $\small \lim_{w\to\infty}\prod_{k=1}^w (p_k-1) $ be determined analytically?

How to check numerical precision of my computation of Stieltjes-constants?

Alternating sums of powers of the lngamma ($\small f_p(x) = \sum \log(k!)^p x^k $ at $\small x=-1$)

Is there a systematic relation between the generating functions for the rows vs that for columns of infinite sized Carleman-matrices?

What would be a better method for numerical diagonalization of a certain Vandermonde-like matrix?

What is the (fractional) half-derivative of zeta at $s=0$ (and how to compute it)?

Who defined the term "Carleman-matrix" and also their properties as they are?

Fractional iteration of a variant of the $\sin()$ function - how to fractionally iterate $ f(x)=\sum_{k=1}^\infty (-1)^k a_{2k}x^{2k}$?

Question about a set of Laplace-transforms

Is my ansatz for finding $n$-periodic-points of the exponential-function exhaustive?

A Zsigmondy-theorem-analogy in the generalized Collatz-problem $3x+\rho$?

Any possible way to invert a function built from a sum of two?

What are conditions to make f(x) defined by f(x)=f(x-1)*x + 1/e unique(for instance convex)?

Efficient way for computation of derivatives of $f(x) = \zeta(1-x) + 1/x $ at integer x?

Is there an option to handle Neumann-series when it diverges? (using infinite-sized Carleman matrices)

On the relevance of the property $\exp^{\circ a}(\exp^{\circ b}(z))=\exp^{\circ a+b}(z)$ for the fractional iteration ("tetration")