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Interesting 31 Bountied Hot Week Month
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Eigenvalues of $A+cd^T$ without determinants

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user1551
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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
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3 votes
3 answers
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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
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6 votes
2 answers
144 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
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11 views

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

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Amrut Ayan
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2 votes
3 answers
99 views

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

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Poonguzhali Annadurai
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3 votes
5 answers
98 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
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2 votes
1 answer
26 views

What is the number of such circular arrangements?

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Thehanna
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1 vote
1 answer
104 views

Solve the diophantine equation involving floor function

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John Omielan
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13 votes
4 answers
1k views

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

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Poonguzhali Annadurai
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3 votes
1 answer
335 views

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

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The Amplitwist
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13 votes
3 answers
1k views

A Pell equation inside a Pell equation

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The Amplitwist
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1 vote
0 answers
18 views

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

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Pelota
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0 votes
1 answer
262 views

Exterior derivative characterization via generators?

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cloudri
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13 votes
4 answers
1k views

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

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Dang Dang
  • 131
-1 votes
0 answers
94 views

On counting rational numbers

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Matteo
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0 votes
2 answers
2k views

Find the Lipschitz constant for the following function

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2 votes
2 answers
1k views

Generalization of Lipschitz continuity to higher order polynomials?

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mathreadler
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0 answers
4 views

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

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Medo
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90 votes
3 answers
8k views

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

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Martin.s
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4 votes
1 answer
92 views

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

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Hjalmar Rosengren
  • 362
0 votes
0 answers
7 views

Jacobi Field Growth and Compactness under Sectional Curvature Bounds

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alpha leonhard
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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
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0 votes
0 answers
24 views

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

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Dang Dang
  • 131
0 votes
0 answers
23 views

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

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ARYAAAAAN
  • 1,622
2 votes
0 answers
40 views

Cyclic sum of adjacent positive integers are power of 2

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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
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2 votes
1 answer
44 views

Bounds for derivatives of smooth function

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Martin R
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0 votes
0 answers
24 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
52 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

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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
22 views

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

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

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

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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?

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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 $2|a+b|$

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Hari Shankar
  • 4,026
2 votes
2 answers
1k views

Integral domain without unity has prime characteristic?

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Davood Solati
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3 votes
1 answer
46 views

Exponential Rate Analog of Berry-Esseen.

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dvitek
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3 votes
3 answers
693 views

Characteristic of a Non-unital Integral Ring

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Davood Solati
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0 votes
2 answers
28 views

The order 4 isometry of the tetrahedron

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Dang Dang
  • 131
2 votes
3 answers
592 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
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2 votes
2 answers
111 views

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

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Hari Shankar
  • 4,026
0 votes
1 answer
1k views

Linear programming - Maximizing negative objective function

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CommunityBot
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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?

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meth-
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1 vote
2 answers
43 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
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0 votes
0 answers
7 views

Question about singular matrix in thin-plate spline interpolation

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mostsquares
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13 votes
4 answers
40k views

Proof that Newton Raphson method has quadratic convergence

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Venkata Karthik Bandaru
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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 $f^{-1}(A)$?

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Daniel Donnelly
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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
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0 votes
0 answers
7 views

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

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user594147
  • 177
0 votes
1 answer
18 views

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

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MathInquirer
  • 588
2 votes
0 answers
20 views

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

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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
144 views

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

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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
32 views
+50

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

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e_s_
  • 1,751
1 vote
0 answers
21 views

Evans' PDE: proof theorem 2 section 5.9

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A rural reader
  • 2,830
12 votes
1 answer
641 views
+100

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

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Jorge Layja
  • 3,924
2 votes
2 answers
556 views

Prove that the length of the common chord is $\frac{2ab\sin \theta}{\sqrt{a^2+b^2+2ab\cos \theta}}$

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Cuckoo Beats
  • 261
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
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2 votes
1 answer
965 views

Semi filled barrel - pt 2

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CommunityBot
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3 votes
2 answers
118 views
+50

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

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Andrew
  • 2,098
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?

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Aristotle
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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
30 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?

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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

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Dan
  • 33.8k
1 vote
0 answers
22 views

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

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user1289267
  • 11
2 votes
0 answers
51 views

An Inequality Conjecture in Harmonic Analysis

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skewray
  • 21
1 vote
0 answers
27 views

Deforming Contour in Method Of Steepest Descent

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Arbuja
  • 105
0 votes
0 answers
28 views

Recurrence relation between $n^{-1}$ and $(n+1)^{-1}$ in GF(p)

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Arbuja
  • 105
1 vote
1 answer
4k views

The advantage of B-spline compared to Bézier if the number of control points is very small

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CommunityBot
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0 votes
0 answers
34 views

Finding the maximum of y in $\frac{x^a+1}{b^x}+\frac{x^b+2}{c^x}+\frac{x^c+3}{a^x}=y$ within a quadrant

d30's user avatar
d30
  • 9
12 votes
1 answer
8k views

How to find the degree of the differential equation $e^{y’}=y+x^5+x^3+x$?

Integreek's user avatar
Integreek
  • 7,794
1 vote
1 answer
168 views

Maximum radius of intersection of a plane and an ellipsoid

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Rodrigo de Azevedo
  • 1
3 votes
2 answers
3k views

Find the points of the ellipsoid $x^2+2y^2+3z^2 = 1$ which are closest to and furthest from the plane $x+y+z=10$

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Rodrigo de Azevedo
  • 1
0 votes
1 answer
108 views

Is every poset with this property already a lattice?

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Keith Kearnes
  • 14.9k
0 votes
1 answer
78 views

Is the derivative of $t^{1/2}\tanh(t^{1/2})$ is completely monotone on $(0,\infty)$?

K B Dave's user avatar
K B Dave
  • 9,016
3 votes
2 answers
971 views

A problem of permutations using the probabilistic method.

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Xiangyu Li
  • 1
0 votes
0 answers
14 views

Analog to discriminant for ratio of polynomials and fractional powers of polynomials

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Gabriel Myers
  • 13
0 votes
0 answers
35 views

f(x) bijections on modulo integer groups

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dandadan
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