User Américo Tavares

59 votes

3 answers

17k views

What is the importance of Calculus in today's Mathematics?

asked Aug 17, 2011 at 17:02

49 votes

6 answers

19k views

Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?

asked Apr 27, 2013 at 20:47

45 votes

6 answers

23k views

What does closed form solution usually mean?

asked Nov 6, 2010 at 20:09

34 votes

11 answers

15k views

How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$?

asked Oct 24, 2010 at 16:57

29 votes

3 answers

3k views

Asymptotic (divergent) series

asked Mar 23, 2012 at 15:21

24 votes

6 answers

2k views

Exercise from Comtet's Advanced Combinatorics: prove $27\sum_{n=1}^{\infty }1/\binom{2n}{n}=9+2\pi \sqrt{3}$

asked Nov 12, 2010 at 21:12

23 votes

8 answers

7k views

Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$?

asked Aug 24, 2010 at 21:59

22 votes

3 answers

2k views

Generalizing $\sum \limits_{n=1}^{\infty }n^{2}/x^{n}$ to $\sum \limits_{n=1}^{\infty }n^{p}/x^{n}$

asked Sep 8, 2010 at 23:31

21 votes

2 answers

19k views

Induction on two integer variables

asked Oct 24, 2010 at 8:57

20 votes

0 answers

473 views

Convergence acceleration technique for $\zeta(4)$ (or $\eta(4)$) via creative telescoping?

asked May 14, 2017 at 19:36

18 votes

7 answers

3k views

Applications of Fractional Calculus

asked Oct 20, 2010 at 14:35

16 votes

2 answers

9k views

How do I prove this sum is not an integer

asked Sep 22, 2010 at 14:57

15 votes

6 answers

13k views

Prerequisites for learning (basic) Graph Theory

asked Sep 10, 2010 at 11:48

15 votes

1 answer

8k views

A series expansion for $\cot (\pi z)$

asked Aug 28, 2010 at 7:48

13 votes

6 answers

3k views

How does one read aloud Vinogradov's notation $\ll$ and $\ll_{\epsilon }$?

asked Sep 20, 2012 at 14:56

12 votes

1 answer

2k views

Methods to find the limit of a sequence defined by a recurrence

asked Nov 15, 2010 at 10:14

11 votes

1 answer

1k views

A limit and a coordinate trigonometric transformation of the interior points of a square into the interior points of a triangle

asked Oct 25, 2010 at 14:44

10 votes

3 answers

2k views

Minimal Ellipse Circumscribing A Right Triangle

asked Aug 28, 2010 at 9:48

10 votes

2 answers

2k views

Binomial coefficients: how to prove an inequality on the $p$-adic valuation?

asked Aug 19, 2010 at 11:31

10 votes

1 answer

1k views

How do I prove the partial denominators formula of the Bauer-Muir transformation of a generalized continued fraction?

asked Sep 14, 2010 at 10:13

10 votes

2 answers

3k views

Do Vector Calculus Cartesian coordinates identities with Div, Grad, Curl hold in cylindrical and spherical coordinates?

asked Oct 12, 2010 at 15:32

9 votes

1 answer

475 views

Estimates for Stirling's formula remainder

asked Dec 2, 2010 at 13:40

9 votes

1 answer

4k views

Convergence tests for improper multiple integrals

asked Dec 22, 2010 at 23:58

8 votes

1 answer

366 views

Which is the Abel's theorem invoked in the context of convergence of this infinite product?

asked Apr 25, 2011 at 11:53

8 votes

1 answer

458 views

Is it right that the fundamental recurrence of an arbitrary continued fraction cannot be proved without induction?

asked Sep 4, 2011 at 10:14

7 votes

1 answer

279 views

Diagonal of the double sequence $(n+1)v_{h,n+1}-(2h+1)v_{h,n}-nv_{h,n-1}=0$

asked Feb 28, 2011 at 14:32

7 votes

1 answer

930 views

Problem from Victor Prasolov's Polynomials -- Finding the number of real roots of $nx^{n}-x^{n-1}-\cdots -1$

asked Nov 19, 2010 at 10:43

7 votes

3 answers

7k views

What is Modern Mathematics? Is this an exact concept with a clear meaning? [closed]

asked Aug 27, 2010 at 6:33

6 votes

2 answers

3k views

Deriving volume of parallelepiped as a function of edge lengths and angles between the edges

asked Sep 12, 2010 at 12:08

6 votes

2 answers

3k views

Evaluating a convergent improper triple integral over the unit sphere

asked Sep 2, 2010 at 21:15

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38 Questions

What is the importance of Calculus in today's Mathematics?

Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?

What does closed form solution usually mean?

How to prove $\cos \frac{2\pi }{5}=\frac{-1+\sqrt{5}}{4}$?

Asymptotic (divergent) series

Exercise from Comtet's Advanced Combinatorics: prove $27\sum_{n=1}^{\infty }1/\binom{2n}{n}=9+2\pi \sqrt{3}$

Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$?

Generalizing $\sum \limits_{n=1}^{\infty }n^{2}/x^{n}$ to $\sum \limits_{n=1}^{\infty }n^{p}/x^{n}$

Induction on two integer variables

Convergence acceleration technique for $\zeta(4)$ (or $\eta(4)$) via creative telescoping?

Applications of Fractional Calculus

How do I prove this sum is not an integer

Prerequisites for learning (basic) Graph Theory

A series expansion for $\cot (\pi z)$

How does one read aloud Vinogradov's notation $\ll$ and $\ll_{\epsilon }$?

Methods to find the limit of a sequence defined by a recurrence

A limit and a coordinate trigonometric transformation of the interior points of a square into the interior points of a triangle

Minimal Ellipse Circumscribing A Right Triangle

Binomial coefficients: how to prove an inequality on the $p$-adic valuation?

How do I prove the partial denominators formula of the Bauer-Muir transformation of a generalized continued fraction?

Do Vector Calculus Cartesian coordinates identities with Div, Grad, Curl hold in cylindrical and spherical coordinates?

Estimates for Stirling's formula remainder

Convergence tests for improper multiple integrals

Which is the Abel's theorem invoked in the context of convergence of this infinite product?

Is it right that the fundamental recurrence of an arbitrary continued fraction cannot be proved without induction?

Diagonal of the double sequence $(n+1)v_{h,n+1}-(2h+1)v_{h,n}-nv_{h,n-1}=0$

Problem from Victor Prasolov's Polynomials -- Finding the number of real roots of $nx^{n}-x^{n-1}-\cdots -1$

What is Modern Mathematics? Is this an exact concept with a clear meaning? [closed]

Deriving volume of parallelepiped as a function of edge lengths and angles between the edges

Evaluating a convergent improper triple integral over the unit sphere