User TheOutZ

11 votes

1 answer

226 views

Non-$\zeta$ term of the sum $\sum\limits_{k = 1}^{\infty} \frac{H_k H_{k+m}}{k^2}$ for $m \in \mathbb{N}_0$

asked Feb 9 at 13:23

8 votes

0 answers

89 views

What number of group elements of a specific order are (non-)realisable?

asked Nov 15, 2022 at 18:36

6 votes

1 answer

696 views

Potential error in the paper: "Every positive integer is the sum of three palindromes"

asked Jan 26, 2019 at 0:27

6 votes

1 answer

372 views

Property of Markov chains when conditioning on zero-probability event

asked Mar 13, 2022 at 9:54

5 votes

3 answers

142 views

Closed form of the recursion formula for $\int_{0}^{1} \ln^r(1-x)x^n \, dx$

asked Mar 7 at 10:09

4 votes

1 answer

187 views

Egyptian unit decomposition + coverings of $\mathbb{Z}_P$ by arithmetic progressions

asked Jun 10, 2022 at 17:29

4 votes

0 answers

79 views

Entire non-constant function $f: \mathbb{C} \rightarrow \mathbb{C}$ such that $f(cz) = f(z)$ [duplicate]

asked Dec 27, 2020 at 21:11

3 votes

1 answer

84 views

Iterated polynomials modulo $p$ and divisibility properties

asked Mar 28, 2021 at 20:18

3 votes

1 answer

56 views

Integrating density over measurable sets yields probability?

asked Mar 6, 2022 at 15:50

2 votes

1 answer

101 views

Why is the matrix defined by $\left(\sum\limits_{k = -N}^{N}\exp(2\pi \textbf{i} k\frac{i-j}{M})\right)_{i,j=1,\ldots,M}$ of rank $2N+1$?

asked Nov 13, 2022 at 10:13

2 votes

2 answers

53 views

Analytic proof: $\frac{2}{t^2}-\frac{\frac{1}{2}\cos(\frac{t}{2})}{\sin^2(\frac{t}{2})} \geq 0$ for $t \in [0,\pi]$?

asked Apr 17, 2022 at 8:51

2 votes

2 answers

2k views

Proof of Cauchy-Schwarz inequality for conditional expectations

asked Jul 20, 2021 at 17:49

2 votes

2 answers

56 views

If $(X,Y)$, $(X',Y')$ are iid. real-valued RV, is $\mathbb{E}(X \cdot Y) = \mathbb{E}(X' \cdot Y')$?

asked Mar 5, 2022 at 13:42

2 votes

0 answers

66 views

Can the generating function $\sum_{n = 1}^{\infty} H_n^k z^n$ for $k \in \mathbb{N}$ generally be determined by special functions?

asked Feb 23 at 19:48

2 votes

0 answers

124 views

Chain rule for matrix derivatives & multiplication of matrix with rank-3-tensor

asked Dec 25, 2022 at 13:37

2 votes

1 answer

133 views

GAP: How to find a (possibly non-minimal) transitive representation of a group?

asked Jun 6 at 23:19

2 votes

1 answer

109 views

When does a finite (transitive) subgroup $G \leq S_n$ admit a "nice" resolvent invariant?

asked Jun 12 at 15:06

1 vote

2 answers

78 views

When is $\{x^2+y^k \mod n: x,y \in \mathbb{Z}/n\mathbb{Z}\} \neq \mathbb{Z}/n\mathbb{Z}$?

asked May 4 at 23:40

1 vote

1 answer

176 views

Mercer's theorem: Complex version

asked Nov 21, 2022 at 10:56

1 vote

1 answer

133 views

Irreducible polynomials for that each output is divisible by an integer n

asked May 22, 2019 at 19:26

1 vote

1 answer

220 views

Wedge Product: Vectors wedged with Multivectors? (Disclaimer: Music theory ahead)

asked Aug 26, 2019 at 15:49

1 vote

0 answers

41 views

How do I integrate a not necessarily differentiable multivariate (Riemann)-Stieltjes integral?

asked Mar 7, 2022 at 11:58

0 votes

2 answers

153 views

Does there exist a stochastic matrix $P$ such that $\ker(P-I)$ contains no nonnegative vector?

asked Mar 22, 2022 at 14:44

0 votes

1 answer

146 views

Piecewise differentiable version: Total variation expressed as an integral

asked Apr 17, 2022 at 9:06

0 votes

1 answer

54 views

Markov property and homogeneity for "arbitrary" measurable set left and right of condition

asked Aug 30, 2021 at 17:05

0 votes

1 answer

74 views

Show that $C(I)^n$ is a Banach space under the following norm

asked Dec 4, 2021 at 21:05

0 votes

2 answers

42 views

Integer polynomials with translation of the constant term - Are these examples unique?

asked Jan 18, 2022 at 18:26

0 votes

0 answers

41 views

Quadratic form $x^2+3y^2$ and non-representability of $2$

asked Dec 25, 2022 at 23:41

0 votes

0 answers

35 views

Relationship between (complete) Bell polynomials and Harmonic numbers - alternative proof

asked Mar 7 at 16:38

-2 votes

1 answer

238 views

The axiom of regularity and "every element is also a set" [ZFC]

asked Oct 28, 2017 at 12:36

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30 Questions

Non-$\zeta$ term of the sum $\sum\limits_{k = 1}^{\infty} \frac{H_k H_{k+m}}{k^2}$ for $m \in \mathbb{N}_0$

What number of group elements of a specific order are (non-)realisable?

Potential error in the paper: "Every positive integer is the sum of three palindromes"

Property of Markov chains when conditioning on zero-probability event

Closed form of the recursion formula for $\int_{0}^{1} \ln^r(1-x)x^n \, dx$

Egyptian unit decomposition + coverings of $\mathbb{Z}_P$ by arithmetic progressions

Entire non-constant function $f: \mathbb{C} \rightarrow \mathbb{C}$ such that $f(cz) = f(z)$ [duplicate]

Iterated polynomials modulo $p$ and divisibility properties

Integrating density over measurable sets yields probability?

Why is the matrix defined by $\left(\sum\limits_{k = -N}^{N}\exp(2\pi \textbf{i} k\frac{i-j}{M})\right)_{i,j=1,\ldots,M}$ of rank $2N+1$?

Analytic proof: $\frac{2}{t^2}-\frac{\frac{1}{2}\cos(\frac{t}{2})}{\sin^2(\frac{t}{2})} \geq 0$ for $t \in [0,\pi]$?

Proof of Cauchy-Schwarz inequality for conditional expectations

If $(X,Y)$, $(X',Y')$ are iid. real-valued RV, is $\mathbb{E}(X \cdot Y) = \mathbb{E}(X' \cdot Y')$?

Can the generating function $\sum_{n = 1}^{\infty} H_n^k z^n$ for $k \in \mathbb{N}$ generally be determined by special functions?

Chain rule for matrix derivatives & multiplication of matrix with rank-3-tensor

GAP: How to find a (possibly non-minimal) transitive representation of a group?

When does a finite (transitive) subgroup $G \leq S_n$ admit a "nice" resolvent invariant?

When is $\{x^2+y^k \mod n: x,y \in \mathbb{Z}/n\mathbb{Z}\} \neq \mathbb{Z}/n\mathbb{Z}$?

Mercer's theorem: Complex version

Irreducible polynomials for that each output is divisible by an integer n

Wedge Product: Vectors wedged with Multivectors? (Disclaimer: Music theory ahead)

How do I integrate a not necessarily differentiable multivariate (Riemann)-Stieltjes integral?

Does there exist a stochastic matrix $P$ such that $\ker(P-I)$ contains no nonnegative vector?

Piecewise differentiable version: Total variation expressed as an integral

Markov property and homogeneity for "arbitrary" measurable set left and right of condition

Show that $C(I)^n$ is a Banach space under the following norm

Integer polynomials with translation of the constant term - Are these examples unique?

Quadratic form $x^2+3y^2$ and non-representability of $2$

Relationship between (complete) Bell polynomials and Harmonic numbers - alternative proof

The axiom of regularity and "every element is also a set" [ZFC]