Américo Tavares

Queluz, Portugal

http://problemasteoremas.wordpress.com

I am a Portuguese electrical engineer, already retired. My Math blog is Problemas e Teoremas.

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

calculus multivariable-calculus soft-question education math-history asked Aug 17, 2011 at 17:02

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50 votes

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

algebra-precalculus number-theory diophantine-equations asked Apr 27, 2013 at 20:47

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45 votes

What does closed form solution usually mean?

soft-question terminology definition closed-form asked Nov 6, 2010 at 20:09

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34 votes

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

geometry trigonometry euclidean-geometry asked Oct 24, 2010 at 16:57

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30 votes

Asymptotic (divergent) series

real-analysis sequences-and-series reference-request divergent-series asked Mar 23, 2012 at 15:21

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24 votes

How to draw these (closed contours) diagrams using TikZ or PSTricks?

tikz-pgf pstricks asked Oct 18, 2012 at 11:34

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24 votes

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

combinatorics sequences-and-series binomial-coefficients asked Nov 12, 2010 at 21:12

math.stackexchange.com

23 votes

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

calculus approximation gamma-function numerical-methods special-functions asked Aug 24, 2010 at 21:59

math.stackexchange.com

22 votes

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

calculus sequences-and-series asked Sep 8, 2010 at 23:31

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22 votes

Induction on two integer variables

induction asked Oct 24, 2010 at 8:57

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Top Answers

252

The Basel problem

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What is the Jacobian matrix?

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Nice proofs of $\zeta(4) = \frac{\pi^4}{90}$?

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What is the result of $\infty - \infty$?

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Evaluation of Gaussian integral $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx$

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Is there a general formula for solving Quartic (Degree $4$) equations?

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Teenager solves Newton dynamics problem - where is the paper?

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Explain $\iint \mathrm dx\,\mathrm dy = \iint r \,\mathrm \,d\alpha\,\mathrm dr$

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Integral of $\frac{1}{(1+x^2)^2}$

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Do foreign acronyms take a definite article, and of which gender?

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Tall fraction puzzle

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Prove: $\int_0^1 \frac{\ln x }{x-1} d x=\sum_1^\infty \frac{1}{n^2}$

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Is there a way to determine how many digits a power of 2 will contain?

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How to draw the calculation of a determinant?

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Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$

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Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?

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O que é e como se pronuncia "fixe"?

portuguese.stackexchange.com

How to create posters using LaTeX

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Adding powers of $i$

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Continued fraction for $\frac{1}{e-2}$

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ISO: cross product

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Orthogonal projection of a point onto a line

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Computing $\zeta(6)=\sum\limits_{k=1}^\infty \frac1{k^6}$ with Fourier series.

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How to determine if a function is one-to-one?

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What is the difference between \over and \frac?

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Inverse of $y = x^3 + x $?

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Rational Numbers - LCM and HCF

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Deriving a trivial continued fraction for the exponential

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Apéry's constant ($\zeta(3)$) value

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Why can ALL quadratic equations be solved by the quadratic formula?

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