# user91500

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bio website location Deutschland age 23 member for 1 year, 3 months seen yesterday profile views 1,179

I am currently a graduate student of $\color{red}{\text{Analytic Number Theory}}$.

I also have a blog.

 14 Is there an elementary proof for Euler's product for Sine? 11 Is $\sum_{k=1}^{m-1}\frac{1}{\sin^2\frac{k\pi}{m}}=\frac{m^2-1}{3}$ true for $m\in\mathbb N$? 10 Euler totient variation identity 10 Proving $\displaystyle\int_0^1\frac{\ln(x)}{x^2-1}\,\mathrm dx=\frac{\pi^2}{8}$ 9 Evaluate the sum of the series

# 4,950 Reputation

 +10 Prove that $2\sum_{k=1}^n \cos(kθ) = \frac{\sin[\left(n+1/2\right)θ]}{\sin(θ/2)}-1$ +10 Simple Divisor Summation Inequality (with Moebius function) +30 Using probability methods prove $\frac{\sin(t)}{t} = \prod_{i=1}^{\infty} \cos \left( \frac{t}{2^i}\right )$ +10 Proof of $(a+b)^{n+1}$

# 26 Questions

 28 Evaluating $‎\sum_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$ 17 Closed form for $\int_{0}^{1/2}\left(2x - 1\right)^{6}\ \log^{2}\left(2\sin\left(\pi x\right)\right)\,{\rm d}x$ 14 Prove that $\sum_{n=1}^{\infty}\frac{(-1)^n}{n}\left\lfloor\frac{\log(n)}{\log(2)}\right\rfloor=\gamma$ 14 Closed form of $\int_0^\frac{1}{2}x^n\cot(\pi x)\,dx$ 13 Prove $\sum_{n=1}^\infty\frac{H_{2n+1}}{n^2}=\frac{11}{4}\zeta(3)+\zeta(2)+4\log(2)-4$

# 57 Tags

 71 calculus × 19 33 limits × 7 51 sequences-and-series × 19 23 power-series × 3 42 trigonometry × 9 21 integration × 8 35 elementary-number-theory × 8 21 real-analysis × 5 34 summation × 8 20 number-theory × 6

# 16 Accounts

 Mathematics 4,950 rep 61544 Area 51 151 rep 2 MathOverflow 103 rep 4 Stack Overflow 101 rep 2 TeX - LaTeX 101 rep 1