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### Questions (57)

 57 How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$? 40 Prime powers, patterns similar to $\lbrace 0,1,0,2,0,1,0,3\ldots \rbrace$ and formulas for $\sigma_k(n)$ 23 Proving that $\frac{\pi}{4}$$=1-\frac{\eta(1)}{2}+\frac{\eta(2)}{4}-\frac{\eta(3)}{8}+\cdots$ 23 Finding the value of $\sum\limits_{k=0}^{\infty}\frac{2^{k}}{2^{2^{k}}+1}$ 21 Riemann's zeta as a continued fraction over prime numbers.

### Reputation (2,318)

 +5 Are all the zeros of $1-a_2x^2+a_4x^4-a_6x^6+\cdots$ real for $a_{2n}>a_{2(n+1)}$ with $a_{2n+1}=0$ and $a_{2n}>0$? +15 Power series with alternating signs and its zeros. +5 Proving that $\frac{\pi^{3}}{32}=1-\sum_{k=1}^{\infty}\frac{2k(2k+1)\zeta(2k+2)}{4^{2k+2}}$ +5 How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$?

 52 Funny identities 9 Funny identities 8 Proving $\prod_{j=1}^n \left(4-\frac2{j}\right)$ is an integer 8 Golden Number Theory 6 Riemann's zeta as a continued fraction over prime numbers.

### Tags (56)

 22 number-theory × 13 8 algebraic-number-theory 11 prime-numbers × 6 8 diophantine-equations 8 riemann-zeta × 18 6 reference-request × 8 8 continued-fractions × 7 3 complex-analysis × 10 8 combinatorics × 2 2 integration × 6

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