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Neves

Coimbra, Portugal

math.stackexchange.com/users/1747/neves

Age: 47

I'm a software developer interested in the recreational side of mathematics.

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Top Questions
31 votes

How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$?

sequences-and-series trigonometry pi asked Mar 15 at 17:49
math.stackexchange.com

29 votes

Prime powers, patterns similar to $\lbrace 0,1,0,2,0,1,0,3\ldots \rbrace$ and formulas for $\sigma_k(n)$

number-theory real-analysis riemann-zeta asked Dec 29 '10 at 17:36
math.stackexchange.com

20 votes

Finding the value of $\sum\limits_{k=0}^{\infty}\frac{2^{k}}{2^{2^{k}}+1}$

sequences-and-series summation asked Apr 8 at 11:48
math.stackexchange.com

13 votes

Arithmetic of continued fractions, does it exist?

reference-request continued-fractions asked Oct 26 '11 at 10:16
math.stackexchange.com

11 votes

How to prove by arithmetical means that $\sum\limits_{k=1}^\infty \frac{((k-1)!)^2}{(2k)!} =\frac{1}{3}\sum\limits_{k=1}^{\infty}\frac{1}{k^{2}}$

calculus sequences-and-series asked Jan 17 '12 at 10:45
math.stackexchange.com

10 votes

Two Dirichlet's series related to the Divisor Summatory Function and to the Riemann's zeta-function, $\zeta(s)$

sequences-and-series reference-request analytic-number-theory riemann-zeta dirichlet-series asked Oct 17 '11 at 14:45
math.stackexchange.com

8 votes

How to draw a line between two paragraphs of my text?

paragraphs rules asked Oct 13 '10 at 9:38
tex.stackexchange.com

7 votes

Numbers of the form $(p_{1}^{\alpha_{_{_1}}})^{2}+(p_{2}^{\alpha_{_{_2}}})^{2}+\cdots+(p_{n}^{\alpha_{_{_n}}})^{2}=(p_{m}^{\alpha_{_{_m}}})^{2}$

number-theory prime-numbers arithmetic summation asked Nov 5 '12 at 11:31
math.stackexchange.com

7 votes

Proving that $\pi=\sum\limits_{k=0}^{\infty}(-1)^{k}\left(\frac{2^{2k+1}+(-1)^{k}}{(4k+1)2^{4k}}+ \frac{2^{2k+2}+(-1)^{k+1}}{(4k+3)2^{4k+2}}\right)$

sequences-and-series power-series pi transcendental-numbers constants asked Mar 22 at 11:28
math.stackexchange.com

6 votes

Asymptotic density of numbers of the form $p_{1}^{\alpha_{1}^{2}}\cdot p_{2}^{\alpha_{2}^{2}}\cdots p_{k}^{\alpha_{k}^{2}}$

analytic-number-theory asked Oct 19 '11 at 16:58
math.stackexchange.com

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Top Answers