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Interesting 31 Bountied Hot Week Month
4 votes
2 answers
88 views

Proof of the identity $\operatorname{Li}_{s+1}(z) = z\frac{(-1)^{s}}{s!}\int_{0}^{1}\frac{(\ln t)^s}{1-zt}\,\mathrm dt$ for $s=2$

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vishalnaakar25
  • 768
3 votes
3 answers
90 views

Proving directly that, for scalene $\triangle ABC$, the bisector of $\angle A$ and perpendicular bisector of $BC$ meet at a point on the circumcircle

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Nishant Kalonia
  • 359
6 votes
2 answers
142 views

How to evaluate : ${\int_0^1\frac{x\ln \left(\frac{x}{2-x}\right)K(\sqrt{x})}{\sqrt{(2-x)^5}}\,\mathrm{d}x}$

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Claude Leibovici
  • 284k
0 votes
0 answers
10 views

Find all the subsets from a set $\{1,2,3,\cdots,n\}$, which contain only coprime numbers.

Amrut Ayan's user avatar
Amrut Ayan
  • 6,549
2 votes
3 answers
98 views

Evaluate $\int_0^3\sqrt\frac{x^3}{3-x}dx$.

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Poonguzhali Annadurai
  • 911
3 votes
5 answers
97 views

Evaluate $I\left(n\right)=\int_{0}^{\infty}\frac{1}{\left(e^{x}+e^{-x}\right)^{n}}\,\mathrm dx$

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Letac Gérard
  • 3,737
2 votes
1 answer
26 views

What is the number of such circular arrangements?

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Thehanna
  • 146
1 vote
1 answer
104 views

Solve the diophantine equation involving floor function

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John Omielan
  • 52.3k
13 votes
4 answers
1k views

Evaluate $\int_0^1{\frac{y}{\sqrt{y(1-y)}}dy}$

Poonguzhali Annadurai's user avatar
Poonguzhali Annadurai
  • 911
3 votes
1 answer
335 views

Non-Hamiltonian $k$-connected $k$-regular graphs ($k>3$)?

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The Amplitwist
  • 1,113
13 votes
3 answers
1k views

A Pell equation inside a Pell equation

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The Amplitwist
  • 1,113
0 votes
0 answers
18 views

Bound on $L^p$ distance for a Gamma distributed random variable

Pelota's user avatar
Pelota
  • 1,317
0 votes
1 answer
261 views

Exterior derivative characterization via generators?

cloudri's user avatar
cloudri
  • 21
13 votes
4 answers
1k views

Given triangle side lengths $a, b, c$, show that $3\left(a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\right)\geq b\left(a+b-c\right)\left(a-c\right)\left(c-b\right)$

Dang Dang's user avatar
Dang Dang
  • 131
-1 votes
0 answers
93 views

On counting rational numbers

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Matteo
  • 43
0 votes
2 answers
2k views

Find the Lipschitz constant for the following function

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CommunityBot
  • 1
2 votes
2 answers
1k views

Generalization of Lipschitz continuity to higher order polynomials?

mathreadler's user avatar
mathreadler
  • 26.5k
0 votes
0 answers
4 views

How write a mixed $L^p$ norm in the form of iterated $p$-integrals

Medo's user avatar
Medo
  • 3,578
90 votes
3 answers
8k views

Conjecture $\int_0^1\frac{\mathrm dx}{\sqrt{1-x}\ \sqrt[4]x\ \sqrt[4]{2-x\,\sqrt3}}\stackrel?=\frac{2\,\sqrt2}{3\,\sqrt[8]3}\pi$

Martin.s's user avatar
Martin.s
  • 6,471
4 votes
1 answer
92 views

How to prove that $\sum \limits_{k=1}^{n} \frac{(-1)^k}{k^2} \frac{\binom{2n}{n+k}}{\binom{2n}{n}} = -\frac{1}{2} \sum \limits_{k=1}^{n} k^{-2}$?

Hjalmar Rosengren's user avatar
Hjalmar Rosengren
  • 362
0 votes
0 answers
7 views

Jacobi Field Growth and Compactness under Sectional Curvature Bounds

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alpha leonhard
  • 1
5 votes
0 answers
304 views
+50

Extending the special function $G(n)=\prod_{k=1}^{n}k^{k^k}$ to any number

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Thinh Dinh
  • 5,798
3 votes
2 answers
880 views

How many non-congruent triangles can be formed by the vertices of a regular polygon of $n$ sides

David K's user avatar
David K
  • 107k
0 votes
0 answers
24 views

Ternary $1$-RLL encode decode with position-independent primer

Dang Dang's user avatar
Dang Dang
  • 131
0 votes
0 answers
22 views

Confusions about $\mathrm{Spec}(R)$ and algebraic groups

ARYAAAAAN's user avatar
ARYAAAAAN
  • 1,622
2 votes
0 answers
40 views

Cyclic sum of adjacent positive integers are power of 2

Lasting Howling's user avatar
Lasting Howling
  • 95
5 votes
1 answer
1k views

How to solve the eigenvalues of a complex matrix of very high condition number?

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CommunityBot
  • 1
2 votes
1 answer
44 views

Bounds for derivatives of smooth function

Martin R's user avatar
Martin R
  • 125k
0 votes
0 answers
23 views

Characterization of real numbers $ c $ for which $ \hat{\mu}(n) = e^{c i n^2}$ holds for a finite Borel measure $ \mu $ on $ \mathbb{T} $

sata's user avatar
sata
  • 1
1 vote
1 answer
171 views

A deceptive integral $\int{\frac{\sqrt{x-3}}{x+6}}dx$

Integreek's user avatar
Integreek
  • 7,794
1 vote
2 answers
51 views

Find $O(b)$ given that $a^5=e$ and $ab^{-1}a=b^2$

Just a user's user avatar
Just a user
  • 20.2k
2 votes
2 answers
223 views

Points $A,B,C$ and $D$ are collinear. A point $P$ is such that $\cos\angle APC=\frac45$ and $\cos\angle BPD=\frac35$. What is $\sin2\angle BPC$?

Integreek's user avatar
Integreek
  • 7,794
3 votes
1 answer
116 views

Function spaces

Vegetable chicken's user avatar
Vegetable chicken
  • 51
3 votes
1 answer
302 views

What is the degree of the differential equarion $\sin\left(\frac{dy}{dx}\right)=x$?

Integreek's user avatar
Integreek
  • 7,794
1 vote
0 answers
21 views

Identity involving the polylogarithm and $\pi i/ 6$

CarP24's user avatar
CarP24
  • 400
3 votes
2 answers
152 views

Compute $\int_0^{\frac\pi2} \frac1{\sin(x+\frac\pi3)\sin(x+\frac\pi6)} dx$

Integreek's user avatar
Integreek
  • 7,794
6 votes
2 answers
305 views

Is there a direct derivation to show that $\int_0^\infty \frac{1-x(2-\sqrt x)}{1-x^3}dx$ vanishes?

Integreek's user avatar
Integreek
  • 7,794
9 votes
3 answers
240 views

If $\int_a^b\ln\left(\frac{3+3x+x^2}{1+x+x^2}\right)dx=0$, find the value of $2|a+b|$

Hari Shankar's user avatar
Hari Shankar
  • 4,026
2 votes
2 answers
1k views

Integral domain without unity has prime characteristic?

Davood Solati's user avatar
Davood Solati
  • 1
3 votes
1 answer
46 views

Exponential Rate Analog of Berry-Esseen.

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dvitek
  • 556
3 votes
3 answers
693 views

Characteristic of a Non-unital Integral Ring

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Davood Solati
  • 1
0 votes
2 answers
28 views

The order 4 isometry of the tetrahedron

Dang Dang's user avatar
Dang Dang
  • 131
2 votes
3 answers
591 views

In an equilateral triangle, lines are drawn from each vertex to the opposite side. Can there be seven regions of integer area?

Andy's user avatar
Andy
  • 1
2 votes
2 answers
111 views

Evaluate $\sum_{r=1}^{101}(-1)^{r-1}(1+\frac12+\frac13+...+\frac1r){101\choose r}$

Hari Shankar's user avatar
Hari Shankar
  • 4,026
0 votes
1 answer
1k views

Linear programming - Maximizing negative objective function

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CommunityBot
  • 1
1 vote
1 answer
40 views

If $f_n$ converges locally uniformly to $f$ on open unit disc, does the difference quotient converge locally uniformly?

meth-'s user avatar
meth-
  • 193
1 vote
2 answers
40 views

Can an arbitrary partition of the set of infinite binary words be seperated in the supremum by a function on the finite words?

user14111's user avatar
user14111
  • 2,768
3 votes
1 answer
17k views

Ice cream vendor problem

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joseph lee
  • 1
0 votes
0 answers
7 views

Question about singular matrix in thin-plate spline interpolation

mostsquares's user avatar
mostsquares
  • 960
13 votes
4 answers
40k views

Proof that Newton Raphson method has quadratic convergence

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Venkata Karthik Bandaru
  • 1,444
1 vote
0 answers
21 views

Eigenvalues of $A+cd^T$ without determinants

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piero
  • 470
0 votes
0 answers
7 views

If $f(x) = \sum_{b \in B(x)}f_b(x)$ and $B(k) \subset B(k+1)$ while $\sum_{b \in B(k)} f_b(x) \geq \sum_{b \in B(k+1)} f_b(x)$ what is $f^{-1}(A)$?

Daniel Donnelly's user avatar
Daniel Donnelly
  • 22.1k
1 vote
1 answer
132 views

Functions $\mathbb{N}\to\{0,1,2\}$ vs injections $\mathbb{N}\to\mathbb{Z}$

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Lucien Lefèvre
  • 31
1 vote
1 answer
993 views

Transformation of continuous, independent random variables

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CommunityBot
  • 1
0 votes
0 answers
7 views

Eigenvalues of $PA$ with $P$ a projection and $A$ having eigenvalues inside open unit disk

user594147's user avatar
user594147
  • 177
0 votes
1 answer
18 views

If ordinal $\alpha$ isomorphic to subset of ordinal $\beta$ then $\alpha \leq \beta$

MathInquirer's user avatar
MathInquirer
  • 588
2 votes
0 answers
20 views

Zeros of $f(z) = z^5 - ae^z$ in $B(0;1)$ for $a<0$

Timo Chang's user avatar
Timo Chang
  • 81
5 votes
3 answers
89 views

Does $L=\lim_{N\to\infty}N\int_{-N}^{N}\prod_{n=1}^{N}\cos\left(\sqrt{n}x\right)dx$ converge?

Claude Leibovici's user avatar
Claude Leibovici
  • 284k
8 votes
2 answers
89 views

What [is the minimal] differential equation is satisfied by $y = \sum_{n=0}^\infty {x^n}(n!)^{-k}$?

Mason's user avatar
Mason
  • 4,220
4 votes
1 answer
73 views

What is the optimal geometry of a waffle?

vallev's user avatar
vallev
  • 1,133
5 votes
1 answer
143 views

Evaluate $\sum_{n=1}^{\infty} \left( \left(2n-1\right) \left(\frac{1}{n^2} + \frac{1}{(n+1)^2} + \ldots \right)^2 - \frac{2}{n} \right)$

Hamza Ayub's user avatar
Hamza Ayub
  • 173
0 votes
0 answers
12 views

Exact Triangle Sorting for Orthographic Rendering of a Triangulated Surface

Jasper's user avatar
Jasper
  • 239
0 votes
0 answers
31 views
+50

Can a symmetric bilinear form whose matrix representation is unitary be diagonalized wrt an orthogonal basis?

e_s_'s user avatar
e_s_
  • 1,751
1 vote
0 answers
21 views

Evans' PDE: proof theorem 2 section 5.9

A rural reader's user avatar
A rural reader
  • 2,830
12 votes
1 answer
641 views
+100

Calculating $\int_0^1 \frac{\arctan^3(x) \log(x)} x\,\mathrm dx$

Jorge Layja's user avatar
Jorge Layja
  • 3,924
3 votes
1 answer
211 views
+100

Wang–Chin partial order for comparing block matrix capacities

dharr's user avatar
dharr
  • 438
2 votes
1 answer
97 views

Approximate $\sec\left(\frac{\pi}{2}x\right)$ using $\frac{1-ax}{1-x}$

Claude Leibovici's user avatar
Claude Leibovici
  • 284k
70 votes
2 answers
2k views
+250

Are the sums $\sum_{n=1}^{\infty} \frac{1}{(n!)^k}$ transcendental?

MJD's user avatar
MJD
  • 67.4k
2 votes
1 answer
965 views

Semi filled barrel - pt 2

Community's user avatar
CommunityBot
  • 1
3 votes
2 answers
118 views
+50

Why is uniform convergence over $\omega$ not possible for sequences of random variables?

Andrew's user avatar
Andrew
  • 2,098
1 vote
1 answer
189 views

Blow-up of $P^1 \times P^1$ in a point

Arctic Char's user avatar
Arctic Char
  • 16.9k
0 votes
0 answers
20 views

Null Space of Infinite Dimensional Matrix

fs98's user avatar
fs98
  • 1
-1 votes
0 answers
27 views

Negativity of a function involving the logarithmic functions

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qifeng618
  • 2,198
2 votes
2 answers
146 views

Is there a classification system where the sum of the digits are a factor?

Aristotle's user avatar
Aristotle
  • 1
23 votes
3 answers
1k views

Trigonometric Inequality. $\sin{1}+\sin{2}+\ldots+\sin{n} <2$ .

mariko_mapmate's user avatar
mariko_mapmate
  • 11
0 votes
0 answers
30 views

$1/|x|$ interpreted as a distribution and Dirac delta distribution

eraldcoil's user avatar
eraldcoil
  • 3,860
2 votes
1 answer
84 views

Does the set $\{b^n - n \mid n \in \mathbb{N}\}$ always cover the complete residue system modulo a for any positive integers $a, b$?

te4's user avatar
te4
  • 290
0 votes
0 answers
25 views

given the following limit equality, prove the following statement

Tomás's user avatar
Tomás
  • 241
0 votes
1 answer
29 views

Examples of connected graphs that are hard to break (at least 3-connected) and have the following property

eagle I 's user avatar
eagle I
  • 140
2 votes
1 answer
49 views

Probability (or asymptotics) that $G_{n, p}$ is a forest?

Misha Lavrov's user avatar
Misha Lavrov
  • 158k
0 votes
0 answers
35 views

Computing $\pi_{n+1}(S^n)$ with Pontryagin's construction, why can we restrict to positive matrices?

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Siméon Lacherez
  • 1
0 votes
0 answers
17 views

Question on Einstein Notation for Distinct Expressions

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Alex Tudor
  • 1
2 votes
0 answers
26 views

A limit about a disk divided into strips and bars

Dan's user avatar
Dan
  • 33.8k
1 vote
0 answers
22 views

Existence of a harmonic function with prescribed partial derivative in $\mathbb{R}^3$

user1289267's user avatar
user1289267
  • 11
2 votes
0 answers
51 views

An Inequality Conjecture in Harmonic Analysis

skewray's user avatar
skewray
  • 21
1 vote
0 answers
27 views

Deforming Contour in Method Of Steepest Descent

Arbuja's user avatar
Arbuja
  • 105
2 votes
1 answer
84 views

Choiceless cardinal exponentiation

Asaf Karagila's user avatar
Asaf Karagila♦
  • 405k
105 votes
9 answers
13k views

Congruence Arithmetic Laws, e.g. in divisibility by $7$ test

Bill Dubuque's user avatar
Bill Dubuque
  • 281k
1 vote
0 answers
65 views
+50

Open set condition and Hausdorff dimension

Mths's user avatar
Mths
  • 71
0 votes
1 answer
21 views

Conditional expectation of a mixture distribution with measure zero event

Ward Abdullah's user avatar
Ward Abdullah
  • 1
27 votes
2 answers
1k views
+500

About the inequality $\sum \frac{x_j}{1-x_j} \sum \frac{y_j}{1-y_j} \ge \sum \frac{x_j}{1-y_j} \sum \frac{y_j}{1-x_j}$

Christophe Boilley's user avatar
Christophe Boilley
  • 6,540
9 votes
1 answer
160 views

A floor function appeared after integration while solving Laplace’s equation. What happened?

Integreek's user avatar
Integreek
  • 7,794
5 votes
2 answers
151 views

Stuck halfway through this integral $\int \frac{(x-1)\sqrt{x^4+2x^3-x^2+2x+1}}{(x^2(x+1))}dx$

Integreek's user avatar
Integreek
  • 7,794
2 votes
1 answer
213 views
+50

How do you find the range of a multivariable function whose domain is the integers?

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RobPratt
  • 50.6k
0 votes
2 answers
175 views

Key reference book on toric ideals: normal or not? Which definition to follow?

Hola's user avatar
Hola
  • 836
1 vote
1 answer
48 views

Number of ways to fill a static sized list of sets

Mohammad Zakzok's user avatar
Mohammad Zakzok
  • 11
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